A topology is a set of subsets satisfying certain axioms, including closure under arbitrary unions and finite intersections. Is there a term for the weakened structure given by changing closure under arbitrary unions to finite unions?
2026-04-18 23:29:45.1776554985
A weakening of the topology axioms
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The structure is just a lattice of sets, albeit with the restriction that it must contain the empty set. A lattice of sets is simply a lattice whose join and meet are union and intersection, respectively.