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Topic: Open and Shut
Replies: 10   Last Post: Feb 4, 2013 10:50 PM

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Shmuel (Seymour J.) Metz

Posts: 3,338
Registered: 12/4/04
Re: Open and Shut
Posted: Feb 4, 2013 10:50 PM
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In <virgil-8A621F.22345103022013@BIGNEWS.USENETMONSTER.COM>, on
02/03/2013
at 10:34 PM, Virgil <virgil@ligriv.com> said:

>Depends on which topology one has for Q.

You specified "under the order toology" (sic)

>If one uses the order topology on Q, in which a basis of the
>interiors of intervals with ENDPOINTS IN Q, Not in R, then your
>set is not closed in Q.


Look again. Its complement is a union of open sets:
{(x,x+1)\/(-x-1,-x)|x?Q>pi}.

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Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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