# Category:Separated Sets

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This category contains results about Separated Sets in the context of Topology.

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A, B \subseteq S$.

### Definition 1

$A$ and $B$ are **separated (in $T$)** if and only if:

- $A^- \cap B = A \cap B^- = \O$

where $A^-$ denotes the closure of $A$ in $T$, and $\O$ denotes the empty set.

### Definition 2

$A$ and $B$ are **separated (in $T$)** if and only if there exist $U,V\in\tau$ with:

- $A\subset U$ and $U\cap B = \varnothing$
- $B\subset V$ and $V\cap A = \varnothing$

where $\varnothing$ denotes the empty set.

$A$ and $B$ are said to be **separated sets (of $T$)**.

## Pages in category "Separated Sets"

The following 6 pages are in this category, out of 6 total.