Category:Alexandroff Extensions
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This category contains results about Alexandroff Extensions.
Definitions specific to this category can be found in Definitions/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.
Pages in category "Alexandroff Extensions"
The following 12 pages are in this category, out of 12 total.
A
- Alexandroff Extension is Compact
- Alexandroff Extension is Topology
- Alexandroff Extension of Rational Number Space is Biconnected
- Alexandroff Extension of Rational Number Space is Connected
- Alexandroff Extension of Rational Number Space is not Hausdorff
- Alexandroff Extension of Rational Number Space is Sequentially Compact
- Alexandroff Extension of Rational Number Space is T1 Space
- Alexandroff Extension which is T2 Space is also T4 Space