- #1

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Is it true that every open set contains a compact set?

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- Thread starter AxiomOfChoice
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- #1

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Is it true that every open set contains a compact set?

- #2

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Well, the empty set is open. And yes, even the empty set contains a compact set.

- #3

HallsofIvy

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However, I can finish by showing the "easy" part: If A is not empty, then it contains, say, "a". The singleton set "a", since it is finite, is compact.

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