Category:Definitions/Examples of Topological Spaces

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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.