# 2 questions in TOPOLOGY

• November 3rd 2010, 04:03 AM
rqeeb
2 questions in TOPOLOGY
I need your help in these 2 Qs:
the pictureAttachment 19565
• November 3rd 2010, 06:45 AM
Plato
The first problem is proved in two steps.
First, If $B$ is a compact set and $p\notin B$ then there are two disjoint open sets such $B\subset G~\&~p\in H$.

Second, each point in $A$ is not in $B$.
If $a\in A$ use part one to get disjoint open sets $G_a~\&~H_a$.
The compactness of $A$ gives a finite collection of each.
The intersection of the $G_x's$ is open and contains $B$.

Problem #2. Use the co-finite topology to show it is false.
• November 4th 2010, 03:10 AM
rqeeb
thank u
but could u please clear the second question more
• November 4th 2010, 07:07 AM
Drexel28
Quote:

Originally Posted by rqeeb
thank u
but could u please clear the second question more

He's suggesting that you take $\mathbb{R}$ with the cofinite topology. The important thing being that the resulting top. space isn't first countable.