[topology] new kind of separation axiom? where does it fit in?

[nonequilibrium]

Hello,

Just out of curiosity, where would following "seperation axiom" fit in?

Assume a topological space X is T1. We call X okay if for any two closed subsets A and B, there exists an open set U such that B \subset U and A \cap U = \emptyset.

So far I'm only acquainted with the T1, T2, T3 and T4 axioms (and the notion of completely regular in relation to the Urysohn theorem).

 

[micromass]

You mean A and B disjoint right??

Can't you always take U=X\setminus A??

 

[nonequilibrium]

Haha...

(and yes I meant A and B disjoint)

It seems I hadn't thought this one true :) thanks a lot!