Is compactness preserved under function mappings?

[deanslist1411]

1. If A is compact, show that f(A) is compact. Is the converse true?

2. If A is connected, show that f(A) is connected. Is the converse true?

3. If B is closed, show that B inverse is closed.

Any help with any or all of these three would be greatly appreciated.

 

[quasar987]

what is f? is f continuous?

There is a set of forums at the top of the page called Homework Help that is suited for these types of questions. You should start posting there as of now. Don't be surprised if you get a warning from a moderator and your thread is moved to the homework section.

Additionnally, Physicsforum guidelines require that you show us what you've tried before you are eligible to getting help.

 

[quasar987]

And what is A? is it in R? in R^n? Or in a general topological space?

 

[LukeD]

I'm assuming that A and B are subsets of some metric space (if they were in a general topological space, then his #3 would be trivial since that would essentially be the definition of a continuous function)