Category:Definitions/Alexandroff Extensions

This category contains definitions related to Alexandroff Extensions.
Related results can be found in Category:Alexandroff Extensions.

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

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

Let $S^* := S \cup \set p$.

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.