A T0-space is a topological space X = (X,Ω(X)) such that
for every pair of distinct points in the space, there is an open set containing one but not the other: x,y ∈ X ⇒ ∃U ∈ Ω(X)[(x ∈ U and y ∉ U) or (y ∈ U and x ∉ U)].
Let X and Y be T0-spaces. A morphism from X to Y is a function f : X→Y that is continuous: V ∈ Ω(Y) ⇒ f−1[V] ∈ Ω(X).
|Strong amalgamation property||no|
|Epimorphisms are surjective||no|
Remark: The properties given above use an (E,M) factorization system with E = surjective morphisms and M = embeddings.