# 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:

- $\displaystyle \BB = \set {\bigcap \FF: \FF \subseteq \SS, \FF \text{ is finite} }$

That is, $\BB$ is the set of all finite intersections of sets in $\SS$.

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

The **topology generated by $\SS$**, denoted $\map \tau \SS$, is defined as:

- $\displaystyle \map \tau \SS = \set {\bigcup \AA: \AA \subseteq \BB}$

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

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