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 $\struct {S, \tau}$.
Pages in category "Definitions/Examples of Topological Spaces"
The following 4 pages are in this category, out of 4 total.