Category:Definitions/Excluded Point Topology

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This category contains definitions related to Excluded Point Topology.
Related results can be found in Category:Excluded Point Topology.

Let $S$ be a set which is non-empty.

Let $p \in S$ be some particular point of $S$.

We define a subset $\tau_{\bar p}$ of the power set $\powerset S$ as:

$\tau_{\bar p} = \set {A \subseteq S: p \notin A} \cup \set S$

That is, all the subsets of $S$ which do not include $p$, along with the set $S$.

Then $\tau_{\bar p}$ is a topology called the excluded point topology on $S$ by $p$, or just an excluded point topology.