The definition states that for all open coverage of $ X $, there is a finite open undercoverage that also covers X Question: The union of open finites is open, so how can I unite open finites and have a closed one? Would not that be a contradiction?
2026-03-28 13:59:29.1774706369
A contradiction involving the compact set definition
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The only thing that is required is that the union of that finite set of open sets contains $X$, not that it is equal no $X$.
Besides (but hardly relevant here), you seem to believe that a set cannot be both open and closed. Yes, it can.