please:

I need your help in these 2 Qs:

the pictureAttachment 19565

Printable View

- Nov 3rd 2010, 04:03 AMrqeeb2 questions in TOPOLOGY
please:

I need your help in these 2 Qs:

the pictureAttachment 19565 - Nov 3rd 2010, 06:45 AMPlato
The first problem is proved in two steps.

First, If is a compact set and then there are two disjoint open sets such .

Second, each point in is not in .

If use part one to get disjoint open sets .

The compactness of gives a finite collection of each.

The intersection of the is open and contains .

Problem #2. Use the co-finite topology to show it is false. - Nov 4th 2010, 03:10 AMrqeeb
thank u

but could u please clear the second question more - Nov 4th 2010, 07:07 AMDrexel28
He's suggesting that you take with the cofinite topology. The important thing being that the resulting top. space isn't first countable.