# Category:Definitions/Examples of Topological Spaces

This category contains definitions of examples of topological spaces.

Let $S$ be a set.

Let $\tau$ be a topology on $S$.

That is, let $\tau \subseteq \powerset S$ satisfy the open set axioms:

 $(\text O 1)$ $:$ The union of an arbitrary subset of $\tau$ is an element of $\tau$. $(\text O 2)$ $:$ The intersection of any two elements of $\tau$ is an element of $\tau$. $(\text O 3)$ $:$ $S$ is an element of $\tau$.

Then the ordered pair $\struct {S, \tau}$ is called a topological space.

The elements of $\tau$ are called open sets of $\struct {S, \tau}$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Examples of Topological Spaces"

The following 3 pages are in this category, out of 3 total.