Thread: 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

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 .

I must tell you that I find your questions rather odd.
It is clear that set 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, is compact, adds to this question.

I think that you are burden with poor text material.

Do you know what any of the words "compact", "open", "closed", or "bounded" mean?