# Topology question

• Jan 30th 2013, 03:15 PM
willywonk
Topology question
Hey sorry for another post. I'm trying to do an assignment and I really don't understand this question

A intersection B is compact. Let B a subset of R2, be as follows: B = { (x,y) in R2s.t. y = sin(1/x), x>0} U {0,0}.
a. Is B closed?, open?, bounded?, compact?

Can you please explain the answer to me, I'm lost. Thanks a lot
• Jan 30th 2013, 03:58 PM
Plato
Re: Topology question
Quote:

Originally Posted by willywonk
A intersection B is compact. Let B a subset of R2, be as follows: B = { (x,y) in R2s.t. y = sin(1/x), x>0} U {0,0}.
a. Is B closed?, open?, bounded?, compact?

If I were you, I would look at the graph of $\displaystyle y=\sin(1/x),~x>0$.

I must tell you that I find your questions rather odd.
It is clear that set $\displaystyle B$ is clearly not closed (look at the graph).
Therefore it cannot be compact.
It certainly is not open.

As to the idea of bounded, that is not a usual concept considered in topology. But if by bounded you mean that the diameter is finite that clearly it is not bounded.

All of that said, I have no idea what the given, $\displaystyle A\cap B$ is compact, adds to this question.

I think that you are burden with poor text material.
• Feb 16th 2013, 02:05 PM
HallsofIvy
Re: Topology question
Do you know what any of the words "compact", "open", "closed", or "bounded" mean?