Does there exist topological spaces (in general) that are compact, but non-bounded?
I know that all compact sets are bounded in a metric space, but I was wondering if there exist some exotic topological space where this is not the case?
Cheers.
Compact but non-bounded space?
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general-topology
compactness
topological-groups
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4How are you defining *bounded* in general topological spaces? – 2017-01-10
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0If a topology isn't defined by a metric what do you mean by "bounded"? – 2017-01-10
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0I'm not sure if such a concept exists. I guess I should have been clearer - my question implies that there is a generalization of "boundedness" beyond that of metric spaces! – 2017-01-10
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1@Henry1981: There really isn’t a natural generalization of boundedness to topological spaces in general. It is possible to define a notion of total boundedness for uniform spaces. – 2017-01-10
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1You can take a look at [Wikipedia: Bornological spaces](https://en.wikipedia.org/wiki/Bornological_space). – 2017-01-10
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0Cool, thanks alot – 2017-01-10