Thread: continuity in topological spaces

prove that if f:X->Y is continuous and if S is a subspace of X, then the restriction f|s: S->Y is continuous.

how would i go about doing this problem? can i create a mapping from S to X, then say S is open and use the fact that f is continuous?

Originally Posted by squarerootof2

prove that if f:X->Y is continuous and if S is a subspace of X, then the restriction f|s: S->Y is continuous.

how would i go about doing this problem? can i create a mapping from S to X, then say S is open and use the fact that f is continuous?

If U is an open subset of Y then its inverse image is open in X; and , which is relatively open in S. That's all there is to it!