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Per definition the Algebra is stable under finite unions and a $\sigma$-algebra is stable under countable unions.

Is there a similar structure with stability over any union of subsets (including uncountable)? Or does this not make sense for some reason?

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    A topology? ${}$ – 2017-01-05
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    Ah yes, thank you. Make it an answer =) – 2017-01-05

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