diff --git a/src/Spaces/DiracSpace.jl b/src/Spaces/DiracSpace.jl
index e0e10f54..41fdcbe3 100644
--- a/src/Spaces/DiracSpace.jl
+++ b/src/Spaces/DiracSpace.jl
@@ -30,6 +30,8 @@ for TYP in (:DiracSpace,:PointSpace)
         spacescompatible(a::$TYP,b::$TYP) = a.points == b.points
         canonicalspace(a::$TYP) = a
 
+        Base.hash(a::$TYP, h::UInt) = hash(a.points, hash($TYP, h))
+
         union_rule(a::$TYP,b::$TYP) = $TYP(sort(union(a.points,b.points)))
 
         function coefficients(cfs::AbstractVector,fromspace::$TYP,tospace::$TYP)
diff --git a/test/SpacesTest.jl b/test/SpacesTest.jl
index 6c520c1c..e2db7f81 100644
--- a/test/SpacesTest.jl
+++ b/test/SpacesTest.jl
@@ -213,6 +213,24 @@ using Test
             f = Fun(PointSpace(1:4), ones(4))
             @test ApproxFunBase.isconstantfun(f)
         end
+
+        @testset "hash" begin
+            DS = ApproxFunBase.DiracSpace
+            for T in (PointSpace, DS)
+                a, b = T(1:2), T(1:2)
+                @test a == b
+                @test hash(a) == hash(b)
+                @test isequal(a, b)
+                @test length(Set([a, b])) == 1
+                @test Dict(a => 1)[b] == 1
+                @test Set([T(1:2), T(3:4)]) == Set([T(3:4), T(1:2)])
+                @test hash(T(1:2)) != hash(T(3:4))
+                @test T([1, 2]) == T([1.0, 2.0])
+                @test hash(T([1, 2])) == hash(T([1.0, 2.0]))
+            end
+            @test PointSpace(1:2) != DS(1:2)
+            @test hash(PointSpace(1:2)) != hash(DS(1:2))
+        end
     end
 
     @testset "DiracSpace" begin