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Topic: Precompactness
Replies: 9   Last Post: Dec 13, 2012 4:19 PM

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quasi

Posts: 10,232
Registered: 7/15/05
Re: Precompactness
Posted: Dec 11, 2012 4:46 PM
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Virgil wrote:
>Kaba wrote:
>>
>> Let X be a locally compact Hausdorff space. Is every open
>> set of X precompact (compact closure)?

>
>Isn't the whole space, X, an open set with a not necessarily
>compact closure, at least if X is only locally compact?


Yes.

Also, for all positive integers n, R^n is locally compact,
but any unbounded open set is not precomnpact.

quasi



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