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I've been trying to understand $ \Leftarrow $ part of proof from link https://math.stackexchange.com/a/153372/240184

I dont understand why

Hence the closure of F is a subset of F, whence they are in fact equal since a set is always subset of its closure

means that F is closed? I thought that closedness could be proofed by showing openness of closure. Would anyone be so kind as to clearify it for me? Maybe a little bit another way to proof it?

Greetings :)

Community
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Michocio
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1 Answers1

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It sounds like you have a definition mixed up. Generally, closures are not open in connected spaces. They are always closed though, hence the name. The closure of a set always contains that set, so if you show the closure is contained in the set, then you've shown they are equal.

Joe Moeller
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