Category:Countable Open Covers Condition for Separated Sets

This category contains pages concerning Countable Open Covers Condition for Separated Sets:

Let $T = \struct {S, \tau}$ be a topological space.

Let $A, B \subseteq S$

For all $X \subseteq S$, let $X^-$ denote the closure of $X$ in $T$.

Let:

$\UU = \set {U_n : n \in \N}$ be a countable open cover of $A : \forall n \in \N : {U_n}^- \cap B = \O$

Let:

$\VV = \set {V_n : n \in \N}$ be a countable open cover of $B : \forall n \in \N : {V_n}^- \cap A = \O$

Then:

$A$ and $B$ can be separated in $T$