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

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Kaba

Posts: 289
Registered: 5/23/11
Re: Precompactness
Posted: Dec 11, 2012 5:40 PM
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11.12.2012 23:46, quasi wrote:
> 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.


Right, too easy:) Thanks.

--
http://kaba.hilvi.org



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