Thread: Continous function

Let f: (X1,d1) -> (X2, d2) be a continous function. Let C, a subset of X2 be compact.

Is f^-1(C) ("f inverse") compact in X2?

Having trouble finding a counterexample...

Originally Posted by math_help

Let f: (X1,d1) -> (X2, d2) be a continous function. Let C, a subset of X2 be compact.

Is f^-1(C) ("f inverse") compact in X2?

Having trouble finding a counterexample...

I'm assuming that you mean

Consider the function

with the usual metric



The one point set is compact in the range. (It is closed and bounded)

but this set is unbouned and not compact.

What do you mean by saying I assume you mean X1?

Originally Posted by math_help

What do you mean by saying I assume you mean X1?

Is f^-1(C) ("f inverse") compact in X2?

not