# Category:Alexandroff Extensions

This category contains results about Alexandroff Extensions.
Definitions specific to this category can be found in Definitions/Alexandroff Extensions.

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

Let $p$ be a new element not in $S$.

Let $S^* := S \cup \left\{{p}\right\}$.

Let $\tau^*$ be the topology on $S^*$ defined such that $U \subseteq S^*$ is open if and only if:

$U$ is an open set of $T$

or

$U$ is the complement in $T^*$ of a closed and compact subset of $T$.

This topology is called the Alexandroff extension on $S$.

## Source of Name

This entry was named for Pavel Sergeyevich Alexandrov.

## Pages in category "Alexandroff Extensions"

The following 12 pages are in this category, out of 12 total.