Category:Included Set Topology

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This category contains results about Included Set Topology.

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

Let $H \subseteq S$ be some subset of $S$.

We define a subset $\tau_H$ of the power set $\mathcal P \left({S}\right)$ as:

$\tau_H = \left\{{A \subseteq S: H \subseteq A}\right\} \cup \left\{{\varnothing}\right\}$

that is, all the subsets of $S$ which are supersets of $H$, along with the empty set $\varnothing$.

Then $\tau_H$ is a topology called the included set topology on $S$ by $H$, or just an included set topology.

The topological space $T = \left({S, \tau_H}\right)$ is called the included set space on $S$ by $H$, or just an included set space.

Pages in category "Included Set Topology"

The following 4 pages are in this category, out of 4 total.