Category:Examples of Topological Spaces

This category contains 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 the following 3 subcategories, out of 3 total.