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Topic: compact
Replies: 9   Last Post: May 18, 2013 9:56 PM

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quasi

Posts: 10,208
Registered: 7/15/05
Re: compact
Posted: May 16, 2013 3:02 PM
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dullrich wrote:
>quasi wrote:
>>dullrich wrote:
>>>William Elliot wrote:
>>>> A point x is an accumulation point of A
>>>> when for all open U nhood x, U /\ A is infinite.
>>>>
>>>> If S is compact, then every infinite set A has an
>>>> accumulation point.
>>>>
>>>> Proof.
>>>> If not, then for all x, there's some open U_x nhood
>>>> x with finite U /\ A. Since C = { U_x | x in S } covers
>>>> S, there's a finite subcover { U_x1,.. U_xj }
>>>> Thus A = A /\ (U_x1 \/..\/ U_xj }
>>>> = (U_x1 /\ A) \/..\/ (U_xj /\ A),
>>>> is finite,

>>>
>>>"has cardinality less than |A|", not "is finite".

>>
>>Looks like a finite union of finite sets, no?

>
>A typo, sort of. Later in the same post he said
>"is finite", where he should have said "has
>cardinality less than |A|". So I decided to post
>a comment, and then I inserted the comment in
>the wrong place, this paragraph looking so much
>like that paragraph...


Had I read the rest of the post (after your comment),
I might have realized (as William Elliot did) that you
had simply accidentally misplaced your comment.

quasi



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