Re: cofinite topology......
- From: quasi <quasi@xxxxxxxx>
- Date: Fri, 02 Sep 2005 20:43:45 -0700
On Sat, 3 Sep 2005 09:18:56 +0900, "mina_world"
<mina_world@xxxxxxxxxxx> wrote:
>hello.....doctor~
>
>suppose that (X, T) is cofinite topology space.
>(T = {U in X | U^c : finite set or X})
>
>if Y is finite subset of X, int(Y) = empty set.
>
>---------------------------------------------
>is this right ??
Yes, provided X is infinite.
>
>i think........
>if X is finite set, this is wrong.
Right. I mean yes, it's wrong (hehe) -- well, you know what I mean.
>because,
>if X is finite set, (X,T) is discrete topology space.
>so,
>even if Y is finite set, int(Y) = Y.(because, Y is open set)
The above logic is fine.
>
>and i have anothor idea.
>i know that finite set on cofinite topology is closed set.
>so, if Y is finite set, all subset of Y is closed set.
>so, int(Y) = empty set.
Ah, but just because it's closed doesn't mean its interior is empty.
In fact, in this case, Y is both closed and open.
>um.......which of case is right ??
>i am confusing.
You were fine until the end when you fooled yourself somehow.
>so, i need your advice.
>thank you very much for your advice.
quasi
.
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- cofinite topology......
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