Category:Definitions/Particular Point Topology

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Particular Point Topology.
Related results can be found in Category:Particular 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 $\tau_p$ of the power set $\powerset S$ as:

$\tau_p = \set {A \subseteq S: p \in A} \cup \set \O$

that is, all the subsets of $S$ which include $p$, along with the empty set.

Then $\tau_p$ is a topology called the particular point topology on $S$ by $p$, or just a particular point topology.