EmptySet: redefine norm/radius/diameter

src/Sets/EmptySet/diameter.jl

@@ -1,3 +1,4 @@
-function diameter(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the diameter of an empty set is undefined"))
+function diameter(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end

src/Sets/EmptySet/norm.jl

@@ -1,3 +1,4 @@
-function norm(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the norm of an empty set is undefined"))
+function norm(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end

src/Sets/EmptySet/radius.jl

@@ -1,3 +1,4 @@
-function radius(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the radius of an empty set is undefined"))
+function radius(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end

test/Sets/EmptySet.jl

@@ -37,9 +37,9 @@ for N in [Float64, Rational{Int}, Float32]
 
     # an_element/norm/radius/diameter functions
     @test_throws ArgumentError an_element(E)
-    @test_throws ArgumentError norm(E)
-    @test_throws ArgumentError radius(E)
-    @test_throws ArgumentError diameter(E)
+    @test norm(E) == N(0)
+    @test radius(E) == N(0)
+    @test diameter(E) == N(0)
 
     # vertices / vertices_list
     @test collect(vertices(E)) == vertices_list(E) == Vector{Vector{N}}()