# Category:Definitions/Topology Generated by Synthetic Sub-Basis

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This category contains definitions related to Topology Generated by Synthetic Sub-Basis.

Define:

- $\displaystyle \mathcal B = \left\{{\bigcap \mathcal F: \mathcal F \subseteq \mathcal S, \, \mathcal F \text{ is finite}}\right\}$

That is, $\mathcal B$ is the set of all finite intersections of sets in $\mathcal S$.

Note that $\mathcal F$ is allowed to be empty in the above definition.

The **topology generated by $\mathcal S$**, denoted $\tau \left({\mathcal S}\right)$, is defined as:

- $\displaystyle \tau \left({\mathcal S}\right) = \left\{{\bigcup \mathcal A: \mathcal A \subseteq \mathcal B}\right\}$

## Pages in category "Definitions/Topology Generated by Synthetic Sub-Basis"

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