diff --git a/docs/src/lib/interfaces/AbstractCentrallySymmetric.md b/docs/src/lib/interfaces/AbstractCentrallySymmetric.md
index 1a1201eee8..7454835444 100644
--- a/docs/src/lib/interfaces/AbstractCentrallySymmetric.md
+++ b/docs/src/lib/interfaces/AbstractCentrallySymmetric.md
@@ -41,7 +41,7 @@ extrema(::AbstractCentrallySymmetric)
 extrema(::AbstractCentrallySymmetric, ::Int)
 isbounded(::AbstractCentrallySymmetric)
 isempty(::AbstractCentrallySymmetric)
-isuniversal(::AbstractCentrallySymmetric{N}, ::Bool=false) where {N}
+isuniversal(::AbstractCentrallySymmetric, ::Bool=false)
 ```
 
 ## Implementations
diff --git a/docs/src/lib/interfaces/AbstractHyperrectangle.md b/docs/src/lib/interfaces/AbstractHyperrectangle.md
index 25728331d5..aaaca3863e 100644
--- a/docs/src/lib/interfaces/AbstractHyperrectangle.md
+++ b/docs/src/lib/interfaces/AbstractHyperrectangle.md
@@ -26,7 +26,7 @@ This interface defines the following functions:
 
 ```@docs
 □(c, r)
-constraints_list(::AbstractHyperrectangle{N}) where {N}
+constraints_list(::AbstractHyperrectangle)
 extrema(::AbstractHyperrectangle)
 extrema(::AbstractHyperrectangle, ::Int)
 generators(::AbstractHyperrectangle)
diff --git a/docs/src/lib/interfaces/AbstractPolytope.md b/docs/src/lib/interfaces/AbstractPolytope.md
index 2cc8ab49ae..757bea1fee 100644
--- a/docs/src/lib/interfaces/AbstractPolytope.md
+++ b/docs/src/lib/interfaces/AbstractPolytope.md
@@ -35,7 +35,7 @@ This interface defines the following functions:
 ```@docs
 isbounded(::AbstractPolytope)
 isempty(::AbstractPolytope)
-isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N}
+isuniversal(::AbstractPolytope, ::Bool=false)
 volume(::AbstractPolytope)
 ```
 
diff --git a/docs/src/lib/interfaces/AbstractSingleton.md b/docs/src/lib/interfaces/AbstractSingleton.md
index a62c538811..90187a9c63 100644
--- a/docs/src/lib/interfaces/AbstractSingleton.md
+++ b/docs/src/lib/interfaces/AbstractSingleton.md
@@ -27,17 +27,17 @@ This interface defines the following functions:
 center(::AbstractSingleton)
 center(::AbstractSingleton, ::Int)
 element(::AbstractSingleton, ::Int)
-generators(::AbstractSingleton{N}) where {N}
-genmat(::AbstractSingleton{N}) where {N}
+generators(::AbstractSingleton)
+genmat(::AbstractSingleton)
 high(::AbstractSingleton)
 high(::AbstractSingleton, ::Int)
 low(::AbstractSingleton)
 low(::AbstractSingleton, ::Int)
 ngens(::AbstractSingleton)
-radius_hyperrectangle(::AbstractSingleton{N}) where {N}
-radius_hyperrectangle(::AbstractSingleton{N}, ::Int) where {N}
+radius_hyperrectangle(::AbstractSingleton)
+radius_hyperrectangle(::AbstractSingleton, ::Int)
 reflect(::AbstractSingleton)
-vertices(::AbstractSingleton{N}) where {N}
+vertices(::AbstractSingleton)
 vertices_list(::AbstractSingleton)
 ∈(::AbstractVector, ::AbstractSingleton)
 ρ(::AbstractVector, ::AbstractSingleton)
diff --git a/docs/src/lib/sets/Ball2.md b/docs/src/lib/sets/Ball2.md
index a8572432ee..d0df9c32ee 100644
--- a/docs/src/lib/sets/Ball2.md
+++ b/docs/src/lib/sets/Ball2.md
@@ -71,7 +71,7 @@ sample(::LazySet, ::Int)
 CurrentModule = LazySets.Ball2Module
 ```
 ```@docs
-sample(::Ball2{N}, ::Int) where {N}
+sample(::Ball2, ::Int)
 ```
 ```@meta
 CurrentModule = LazySets.API
@@ -187,7 +187,7 @@ CurrentModule = LazySets.API
 CurrentModule = LazySets
 ```
 * [`isempty`](@ref isempty(::AbstractCentrallySymmetric))
-* [`isuniversal`](@ref isuniversal(::AbstractCentrallySymmetric{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractCentrallySymmetric, ::Bool=false))
 
 Inherited from [`AbstractBallp`](@ref):
 * [`high`](@ref high(::AbstractBallp, ::Int))
diff --git a/docs/src/lib/sets/BallInf.md b/docs/src/lib/sets/BallInf.md
index 03cbae9300..a9b74d725e 100644
--- a/docs/src/lib/sets/BallInf.md
+++ b/docs/src/lib/sets/BallInf.md
@@ -148,7 +148,7 @@ Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
 * [`center`](@ref center(::LazySet, ::Int))
 * [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))
 * [`isempty`](@ref isempty(::AbstractCentrallySymmetricPolytope))
-* [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 
 Inherited from [`AbstractZonotope`](@ref):
 * [`order`](@ref order(::AbstractZonotope))
@@ -163,7 +163,7 @@ CurrentModule = LazySets.API
 ```@meta
 CurrentModule = LazySets
 ```
-* [`constraints_list`](@ref constraints_list(::AbstractHyperrectangle{N}) where {N})
+* [`constraints_list`](@ref constraints_list(::AbstractHyperrectangle))
 * [`extrema`](@ref extrema(::AbstractHyperrectangle))
 * [`extrema`](@ref extrema(::AbstractHyperrectangle, ::Int))
 * [`generators`](@ref generators(::AbstractHyperrectangle))
diff --git a/docs/src/lib/sets/Ballp.md b/docs/src/lib/sets/Ballp.md
index 26e52df37a..3a5d1a9d3e 100644
--- a/docs/src/lib/sets/Ballp.md
+++ b/docs/src/lib/sets/Ballp.md
@@ -91,7 +91,7 @@ Inherited from [`AbstractCentrallySymmetric`](@ref):
 * [`isboundedtype`](@ref isboundedtype(::Type{AbstractCentrallySymmetric}))
 * [`isconvextype`](@ref isconvextype(::Type{AbstractCentrallySymmetric}))
 * [`isempty`](@ref isempty(::AbstractCentrallySymmetric))
-* [`isuniversal`](@ref isuniversal(::AbstractCentrallySymmetric{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractCentrallySymmetric, ::Bool=false))
 
 Inherited from [`AbstractBallp`](@ref):
 * [`low`](@ref low(::AbstractBallp, ::Int))
diff --git a/docs/src/lib/sets/Ellipsoid.md b/docs/src/lib/sets/Ellipsoid.md
index 3936cf1bd9..45e4cba05f 100644
--- a/docs/src/lib/sets/Ellipsoid.md
+++ b/docs/src/lib/sets/Ellipsoid.md
@@ -126,4 +126,4 @@ CurrentModule = LazySets.API
 CurrentModule = LazySets
 ```
 * [`isempty`](@ref isempty(::AbstractCentrallySymmetric))
-* [`isuniversal`](@ref isuniversal(::AbstractCentrallySymmetric{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractCentrallySymmetric, ::Bool=false))
diff --git a/docs/src/lib/sets/HParallelotope.md b/docs/src/lib/sets/HParallelotope.md
index a31dca5437..bcf8e86a4d 100644
--- a/docs/src/lib/sets/HParallelotope.md
+++ b/docs/src/lib/sets/HParallelotope.md
@@ -50,7 +50,7 @@ Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
 * [`an_element`](@ref an_element(::AbstractCentrallySymmetricPolytope))
 * [`extrema`](@ref extrema(::AbstractCentrallySymmetricPolytope))
 * [`extrema`](@ref extrema(::AbstractCentrallySymmetricPolytope, ::Int))
-* [`isuniversal`](@ref isuniversal(::AbstractCentrallySymmetricPolytope, ::Bool=false))
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 
 Inherited from [`AbstractZonotope`](@ref):
 * [`isempty`](@ref isempty(::AbstractZonotope))
diff --git a/docs/src/lib/sets/HPolygon.md b/docs/src/lib/sets/HPolygon.md
index 71a432ea1c..2afa3f31ff 100644
--- a/docs/src/lib/sets/HPolygon.md
+++ b/docs/src/lib/sets/HPolygon.md
@@ -29,7 +29,7 @@ Inherited from [`LazySet`](@ref):
 
 Inherited from [`AbstractPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractPolytope))
-* [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))
diff --git a/docs/src/lib/sets/HPolygonOpt.md b/docs/src/lib/sets/HPolygonOpt.md
index dc5219938c..265846f225 100644
--- a/docs/src/lib/sets/HPolygonOpt.md
+++ b/docs/src/lib/sets/HPolygonOpt.md
@@ -18,7 +18,7 @@ Inherited from [`LazySet`](@ref):
 
 Inherited from [`AbstractPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractPolytope))
-* [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))
diff --git a/docs/src/lib/sets/HPolytope.md b/docs/src/lib/sets/HPolytope.md
index 91bbd12dff..f23a12f88e 100644
--- a/docs/src/lib/sets/HPolytope.md
+++ b/docs/src/lib/sets/HPolytope.md
@@ -47,5 +47,5 @@ CurrentModule = LazySets
 ```
 
 Inherited from [`AbstractPolytope`](@ref):
-* [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 * [`volume`](@ref volume(::AbstractPolytope))
diff --git a/docs/src/lib/sets/Hyperrectangle.md b/docs/src/lib/sets/Hyperrectangle.md
index 7b701235ca..66a01d97fa 100644
--- a/docs/src/lib/sets/Hyperrectangle.md
+++ b/docs/src/lib/sets/Hyperrectangle.md
@@ -50,7 +50,7 @@ Inherited from [`AbstractZonotope`](@ref):
 * [`linear_map`](@ref linear_map(::AbstractMatrix, ::AbstractZonotope))
 
 Inherited from [`AbstractHyperrectangle`](@ref):
-* [`constraints_list`](@ref constraints_list(::AbstractHyperrectangle{N}) where {N})
+* [`constraints_list`](@ref constraints_list(::AbstractHyperrectangle))
 * [`extrema`](@ref extrema(::AbstractHyperrectangle))
 * [`extrema`](@ref extrema(::AbstractHyperrectangle, ::Int))
 * [`generators`](@ref generators(::AbstractHyperrectangle))
diff --git a/docs/src/lib/sets/Singleton.md b/docs/src/lib/sets/Singleton.md
index 2f2d52d598..1a9f0b604f 100644
--- a/docs/src/lib/sets/Singleton.md
+++ b/docs/src/lib/sets/Singleton.md
@@ -120,18 +120,18 @@ Inherited from [`AbstractSingleton`](@ref):
 * [`center`](@ref center(::AbstractSingleton))
 * [`center`](@ref center(::AbstractSingleton, ::Int))
 * [`constraints_list`](@ref constraints_list(::AbstractSingleton))
-* [`generators`](@ref generators(::AbstractSingleton{N}) where {N})
-* [`genmat`](@ref genmat(::AbstractSingleton{N}) where {N})
+* [`generators`](@ref generators(::AbstractSingleton))
+* [`genmat`](@ref genmat(::AbstractSingleton))
 * [`high`](@ref high(::AbstractSingleton))
 * [`high`](@ref high(::AbstractSingleton, ::Int))
 * [`isboundedtype`](@ref isboundedtype(::Type{AbstractSingleton}))
 * [`low`](@ref low(::AbstractSingleton))
 * [`low`](@ref low(::AbstractSingleton, ::Int))
 * [`ngens`](@ref ngens(::AbstractSingleton))
-* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton{N}) where {N})
-* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton{N}, ::Int) where {N})
+* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton))
+* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton, ::Int))
 * [`reflect`](@ref reflect(::AbstractSingleton))
-* [`vertices`](@ref vertices(::AbstractSingleton{N}) where {N})
+* [`vertices`](@ref vertices(::AbstractSingleton))
 * [`vertices_list`](@ref vertices_list(::AbstractSingleton))
 * [`∈`](@ref ∈(::AbstractVector, ::AbstractSingleton))
 * [`ρ`](@ref σ(::AbstractVector, ::AbstractSingleton))
diff --git a/docs/src/lib/sets/Universe.md b/docs/src/lib/sets/Universe.md
index e976a32174..9a20ed4843 100644
--- a/docs/src/lib/sets/Universe.md
+++ b/docs/src/lib/sets/Universe.md
@@ -20,7 +20,7 @@ an_element(::LazySet)
 CurrentModule = LazySets.UniverseModule
 ```
 ```@docs
-an_element(::Universe{N}) where {N}
+an_element(::Universe)
 constrained_dimensions(::Universe)
 ```
 ```@meta
diff --git a/docs/src/lib/sets/VPolygon.md b/docs/src/lib/sets/VPolygon.md
index 4526834f16..43f298a195 100644
--- a/docs/src/lib/sets/VPolygon.md
+++ b/docs/src/lib/sets/VPolygon.md
@@ -52,7 +52,7 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isempty`](@ref isempty(::AbstractPolytope))
-* [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))
diff --git a/docs/src/lib/sets/VPolytope.md b/docs/src/lib/sets/VPolytope.md
index 0456160783..7b096b3072 100644
--- a/docs/src/lib/sets/VPolytope.md
+++ b/docs/src/lib/sets/VPolytope.md
@@ -55,5 +55,5 @@ Inherited from [`AbstractPolyhedron`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isempty`](@ref isempty(::AbstractPolytope))
-* [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 * [`volume`](@ref volume(::AbstractPolytope))
diff --git a/docs/src/lib/sets/ZeroSet.md b/docs/src/lib/sets/ZeroSet.md
index accea5c888..d4613c0657 100644
--- a/docs/src/lib/sets/ZeroSet.md
+++ b/docs/src/lib/sets/ZeroSet.md
@@ -11,8 +11,8 @@ ZeroSet
 ## Operations
 
 ```@docs
-element(::ZeroSet{N}) where {N}
-element(::ZeroSet{N}, ::Int) where {N}
+element(::ZeroSet)
+element(::ZeroSet, ::Int)
 ```
 ```@meta
 CurrentModule = LazySets.API
@@ -99,17 +99,17 @@ Inherited from [`AbstractSingleton`](@ref):
 * [`center`](@ref center(::AbstractSingleton))
 * [`center`](@ref center(::AbstractSingleton, ::Int))
 * [`constraints_list`](@ref constraints_list(::AbstractSingleton))
-* [`generators`](@ref generators(::AbstractSingleton{N}) where {N})
-* [`genmat`](@ref genmat(::AbstractSingleton{N}) where {N})
+* [`generators`](@ref generators(::AbstractSingleton))
+* [`genmat`](@ref genmat(::AbstractSingleton))
 * [`high`](@ref high(::AbstractSingleton))
 * [`high`](@ref high(::AbstractSingleton, ::Int))
 * [`isconvextype`](@ref isconvextype(::Type{AbstractSingleton}))
 * [`low`](@ref low(::AbstractSingleton))
 * [`low`](@ref low(::AbstractSingleton, ::Int))
 * [`ngens`](@ref ngens(::AbstractSingleton))
-* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton{N}) where {N})
-* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton{N}, ::Int) where {N})
-* [`vertices`](@ref vertices(::AbstractSingleton{N}) where {N})
+* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton))
+* [`radius_hyperrectangle`](@ref radius_hyperrectangle(::AbstractSingleton, ::Int))
+* [`vertices`](@ref vertices(::AbstractSingleton))
 * [`vertices`](@ref vertices(::AbstractSingleton))
 * [`vertices_list`](@ref vertices_list(::AbstractSingleton))
 * [`σ`](@ref σ(::AbstractVector, ::AbstractSingleton))
diff --git a/docs/src/lib/sets/Zonotope.md b/docs/src/lib/sets/Zonotope.md
index 083b59d409..bab5339380 100644
--- a/docs/src/lib/sets/Zonotope.md
+++ b/docs/src/lib/sets/Zonotope.md
@@ -47,7 +47,7 @@ Inherited from [`LazySet`](@ref):
 
 Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
-* [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
+* [`isuniversal`](@ref isuniversal(::AbstractPolytope, ::Bool=false))
 * [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
diff --git a/src/Interfaces/AbstractCentrallySymmetric.jl b/src/Interfaces/AbstractCentrallySymmetric.jl
index 171f27d94d..ae250904ef 100644
--- a/src/Interfaces/AbstractCentrallySymmetric.jl
+++ b/src/Interfaces/AbstractCentrallySymmetric.jl
@@ -99,8 +99,7 @@ function isempty(::AbstractCentrallySymmetric)
 end
 
 """
-    isuniversal(S::AbstractCentrallySymmetric{N},
-                [witness]::Bool=false) where {N}
+    isuniversal(S::AbstractCentrallySymmetric, [witness]::Bool=false)
 
 Check whether a centrally symmetric set is universal.
 
@@ -120,9 +119,9 @@ Centrally symmetric sets are bounded.
 A witness is obtained by computing the support vector in direction
 `d = [1, 0, …, 0]` and adding `d` on top.
 """
-function isuniversal(S::AbstractCentrallySymmetric{N},
-                     witness::Bool=false) where {N}
+function isuniversal(S::AbstractCentrallySymmetric, witness::Bool=false)
     if witness
+        N = eltype(S)
         d = SingleEntryVector{N}(1, dim(S))
         w = σ(d, S) + d
         return (false, w)
diff --git a/src/Interfaces/AbstractHyperrectangle.jl b/src/Interfaces/AbstractHyperrectangle.jl
index 2774ee799d..c9369bff7e 100644
--- a/src/Interfaces/AbstractHyperrectangle.jl
+++ b/src/Interfaces/AbstractHyperrectangle.jl
@@ -283,7 +283,7 @@ function vertices_list(H::AbstractHyperrectangle; kwargs...)
 end
 
 """
-    constraints_list(H::AbstractHyperrectangle{N}) where {N}
+    constraints_list(H::AbstractHyperrectangle)
 
 Return the list of constraints of a hyperrectangular set.
 
@@ -295,7 +295,7 @@ Return the list of constraints of a hyperrectangular set.
 
 A list of ``2n`` linear constraints, where ``n`` is the dimension of `H`.
 """
-function constraints_list(H::AbstractHyperrectangle{N}) where {N}
+function constraints_list(H::AbstractHyperrectangle)
     return _constraints_list_hyperrectangle(H)
 end
 
diff --git a/src/Interfaces/AbstractPolytope.jl b/src/Interfaces/AbstractPolytope.jl
index b47464f890..310d179273 100644
--- a/src/Interfaces/AbstractPolytope.jl
+++ b/src/Interfaces/AbstractPolytope.jl
@@ -76,7 +76,7 @@ function isempty(P::AbstractPolytope)
 end
 
 """
-    isuniversal(P::AbstractPolytope{N}, [witness]::Bool=false) where {N}
+    isuniversal(P::AbstractPolytope, [witness]::Bool=false)
 
 Check whether a polytopic set is universal.
 
@@ -96,10 +96,11 @@ Check whether a polytopic set is universal.
 A witness is produced using `isuniversal(H)` where `H` is the first linear
 constraint of `P`.
 """
-function isuniversal(P::AbstractPolytope{N}, witness::Bool=false) where {N}
+function isuniversal(P::AbstractPolytope, witness::Bool=false)
     if witness
         constraints = constraints_list(P)
         if isempty(constraints)
+            N = eltype(P)
             return (true, N[])  # special case for polytopes without constraints
         end
         return isuniversal(constraints[1], true)
diff --git a/src/Interfaces/AbstractSingleton.jl b/src/Interfaces/AbstractSingleton.jl
index a1c7ff8747..6d244374bf 100644
--- a/src/Interfaces/AbstractSingleton.jl
+++ b/src/Interfaces/AbstractSingleton.jl
@@ -63,7 +63,7 @@ function element(S::AbstractSingleton, i::Int)
 end
 
 """
-    radius_hyperrectangle(S::AbstractSingleton{N}, i::Int) where {N}
+    radius_hyperrectangle(S::AbstractSingleton, i::Int)
 
 Return the box radius of a set with a single value in a given dimension.
 
@@ -76,13 +76,14 @@ Return the box radius of a set with a single value in a given dimension.
 
 Zero.
 """
-function radius_hyperrectangle(S::AbstractSingleton{N}, i::Int) where {N}
+function radius_hyperrectangle(S::AbstractSingleton, i::Int)
     @boundscheck _check_bounds(S, i)
+    N = eltype(S)
     return zero(N)
 end
 
 """
-    radius_hyperrectangle(S::AbstractSingleton{N}) where {N}
+    radius_hyperrectangle(S::AbstractSingleton)
 
 Return the box radius of a set with a single value in every dimension.
 
@@ -94,7 +95,8 @@ Return the box radius of a set with a single value in every dimension.
 
 The zero vector.
 """
-function radius_hyperrectangle(S::AbstractSingleton{N}) where {N}
+function radius_hyperrectangle(S::AbstractSingleton)
+    N = eltype(S)
     return zeros(N, dim(S))
 end
 
@@ -173,7 +175,7 @@ function low(S::AbstractSingleton, i::Int)
 end
 
 """
-   genmat(S::AbstractSingleton{N}) where {N}
+   genmat(S::AbstractSingleton)
 
 Return the (empty) generator matrix of a set with a single value.
 
@@ -185,12 +187,13 @@ Return the (empty) generator matrix of a set with a single value.
 
 A matrix with no columns representing the generators of `S`.
 """
-function genmat(S::AbstractSingleton{N}) where {N}
+function genmat(S::AbstractSingleton)
+    N = eltype(S)
     return Matrix{N}(undef, dim(S), 0)
 end
 
 """
-    generators(S::AbstractSingleton{N}) where {N}
+    generators(S::AbstractSingleton)
 
 Return an (empty) iterator over the generators of a set with a single value.
 
@@ -202,7 +205,8 @@ Return an (empty) iterator over the generators of a set with a single value.
 
 An empty iterator.
 """
-function generators(S::AbstractSingleton{N}) where {N}
+function generators(S::AbstractSingleton)
+    N = eltype(S)
     return EmptyIterator{Vector{N}}()
 end
 
@@ -260,7 +264,7 @@ function center(S::AbstractSingleton, i::Int)
 end
 
 """
-    vertices(S::AbstractSingleton{N}) where {N}
+    vertices(S::AbstractSingleton)
 
 Construct an iterator over the vertices of a set with a single value.
 
@@ -272,7 +276,7 @@ Construct an iterator over the vertices of a set with a single value.
 
 An iterator with a single value.
 """
-function vertices(S::AbstractSingleton{N}) where {N}
+function vertices(S::AbstractSingleton)
     return SingletonIterator(element(S))
 end
 
diff --git a/src/Sets/Ball2/sample.jl b/src/Sets/Ball2/sample.jl
index 8bbb82fa0d..ac5d3a1af2 100644
--- a/src/Sets/Ball2/sample.jl
+++ b/src/Sets/Ball2/sample.jl
@@ -1,9 +1,9 @@
 """
 # Extended help
 
-    sample(B::Ball2{N}, [nsamples]::Int;
+    sample(B::Ball2, [nsamples]::Int;
            [rng]::AbstractRNG=GLOBAL_RNG,
-           [seed]::Union{Int, Nothing}=nothing) where {N}
+           [seed]::Union{Int, Nothing}=nothing)
 
 ### Algorithm
 
@@ -11,11 +11,12 @@ Random sampling with uniform distribution in `B` is computed using Muller's meth
 of normalized Gaussians. This method requires the package `Distributions`.
 See [`_sample_unit_nball_muller!`](@ref) for implementation details.
 """
-function sample(B::Ball2{N}, nsamples::Int;
+function sample(B::Ball2, nsamples::Int;
                 rng::AbstractRNG=GLOBAL_RNG,
-                seed::Union{Int,Nothing}=nothing) where {N}
+                seed::Union{Int,Nothing}=nothing)
     require(@__MODULE__, :Distributions; fun_name="sample")
     n = dim(B)
+    N = eltype(B)
     D = Vector{Vector{N}}(undef, nsamples) # preallocate output
     _sample_unit_nball_muller!(D, n, nsamples; rng=rng, seed=seed)
 
@@ -28,9 +29,9 @@ function sample(B::Ball2{N}, nsamples::Int;
 end
 
 """
-    _sample_unit_nball_muller!(D::Vector{Vector{N}}, n::Int, p::Int;
+    _sample_unit_nball_muller!(D::Vector{<:Vector}, n::Int, p::Int;
                                [rng]::AbstractRNG=GLOBAL_RNG,
-                               [seed]::Union{Int, Nothing}=nothing) where {N}
+                               [seed]::Union{Int, Nothing}=nothing)
 
 Draw samples from a uniform distribution on an ``n``-dimensional unit ball
 using Muller's method.
@@ -65,9 +66,9 @@ where ``α := \\sqrt{z₁² + z₂² + … + z_n²}``, is uniform over the
 [1] Muller, Mervin E. *A note on a method for generating points uniformly on
     n-dimensional spheres.* Communications of the ACM 2.4 (1959): 19-20.
 """
-function _sample_unit_nball_muller!(D::Vector{Vector{N}}, n::Int, p::Int;
+function _sample_unit_nball_muller!(D::Vector{<:Vector}, n::Int, p::Int;
                                     rng::AbstractRNG=GLOBAL_RNG,
-                                    seed::Union{Int,Nothing}=nothing) where {N}
+                                    seed::Union{Int,Nothing}=nothing)
     return _sample_unit_nball_muller_distributions!(D, n, p; rng=rng, seed=seed)
 end
 
diff --git a/src/Sets/Universe/an_element.jl b/src/Sets/Universe/an_element.jl
index 64898b0eeb..7c0438fd4d 100644
--- a/src/Sets/Universe/an_element.jl
+++ b/src/Sets/Universe/an_element.jl
@@ -1,12 +1,13 @@
 """
 # Extended help
 
-    an_element(U::Universe{N}) where {N}
+    an_element(U::Universe)
 
 ### Algorithm
 
 The output is the origin.
 """
-function an_element(U::Universe{N}) where {N}
+function an_element(U::Universe)
+    N = eltype(U)
     return zeros(N, dim(U))
 end
diff --git a/src/Sets/ZeroSet/element.jl b/src/Sets/ZeroSet/element.jl
index 1c6fa6085d..b125150161 100644
--- a/src/Sets/ZeroSet/element.jl
+++ b/src/Sets/ZeroSet/element.jl
@@ -1,5 +1,5 @@
 """
-    element(Z::ZeroSet{N}) where {N}
+    element(Z::ZeroSet)
 
 Return the element of a zero set.
 
@@ -11,12 +11,13 @@ Return the element of a zero set.
 
 The element of the zero set, i.e., a zero vector.
 """
-function element(Z::ZeroSet{N}) where {N}
+function element(Z::ZeroSet)
+    N = eltype(Z)
     return zeros(N, Z.dim)
 end
 
 """
-    element(Z::ZeroSet{N}, ::Int) where {N}
+    element(Z::ZeroSet, i::Int)
 
 Return the i-th entry of the element of a zero set.
 
@@ -29,6 +30,7 @@ Return the i-th entry of the element of a zero set.
 
 The i-th entry of the element of the zero set, i.e., 0.
 """
-function element(Z::ZeroSet{N}, ::Int) where {N}
+function element(Z::ZeroSet, ::Int)
+    N = eltype(Z)
     return zero(N)
 end