Structures closed under union

Mathematical structures that are closed under countable or uncountable unions often give rise to a maximal structure generated by some set. We would go through examples in topology to explore this idea. This is closely related to structures closed under intersection. Interiors From topology, arbitrary unions of open sets are open by definition. As such for any subset AAA of a topological space XXX we can define the interior of AAA to be Int(A)=⋃F open in X,  F⊂AF\text{Int}(A)=\bigcup_{F \text{ ...

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