- Set - $\tau $
- Generator - basis of $\tau $
- Operator - $\cup $
- Unit - empty set
Is it a monoid?
2026-03-25 06:02:14.1774418534
Is (topology, union, empty set) with basis as generator a monoid?
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No.
A base for a topological space is not necessarily closed under union. For instance, the set of open intervals is a base for the standard topology on $\mathbb{R}$, but the set of open intervals is not closed under union.
However, if the base is closed under union, then it should be a monoid, since set union is an associative operation.