Category:Discrete Topology

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This category contains results about Discrete Topology.
Definitions specific to this category can be found in Definitions/Discrete Topology.


Let $S \ne \O$ be a set.

Let $\tau = \powerset S$ be the power set of $S$.

That is, let $\tau$ be the set of all subsets of $S$:

$\tau := \set {H: H \subseteq S}$


Then $\tau$ is called the discrete topology on $S$ and $\struct {S, \tau} = \struct {S, \powerset S}$ the discrete space on $S$, or just a discrete space.


Finite Discrete Topology

Let $S$ be a finite set.

Then $\tau = \powerset S$ is a finite discrete topology, and $\struct {S, \tau} = \struct {S, \powerset S}$ is a finite discrete space.


Infinite Discrete Topology

Let $S$ be an infinite set.

Then $\tau = \powerset S$ is an infinite discrete topology, and $\struct {S, \tau} = \struct {S, \powerset S}$ is an infinite discrete space.

Subcategories

This category has the following 8 subcategories, out of 8 total.

Pages in category "Discrete Topology"

The following 69 pages are in this category, out of 69 total.