**If f: R^n --> R^m is continuous everywhere and S is bounded, then f(S) is bounded**
I have a general idea on how to go about it; if

is a sequence in

, then it has a subsequence

that converges to some

, and since

is continuous there

is a convergent sequence in

, which means that sequence is bounded. Now I am not sure if I can conclude that

is bounded. If I can't, how would I go about proving that if a function is continuous everywhere and a set S, subset of

, is bounded, then

is bounded? Any help would be appreciated, thanks.