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Math and science::Topology

Subbasis

Let \( X \) be a set. A subbasis for a topology on \( X \) is a collection of subsets of \( X \) whose union equals \( X \).

Let \( \mathcal{S} \) be a subbasis for a topology on \( X \). The set of all [something of something of something] is a topolgy on \( X \). This topology is said to be generated by the subbasis \( \mathcal{S} \).

It can be proved that the generated set forms a valid topology.