Category:Countable Open Covers Condition for Separated Sets
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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 $T$
Pages in category "Countable Open Covers Condition for Separated Sets"
The following 3 pages are in this category, out of 3 total.