Trying to learn topology and need help with this proof

1. Aug 5, 2004

Ed Quanta

If S is a set with the discrete topology and f:S->T is any transformation of S into a topologized set T, then f is continuous.

Can someone help me prove this? I have no idea where to even begin.

2. Aug 5, 2004

matt grime

Def: a map, f, is continuous iff the inverse image of every open set is open. Let U be any subsey of T, f^{-1}(U) is a subset of S. All subsets of S are...?

Just use the definition of continuous

3. Aug 24, 2004

mathwonk

intuitively, "f is continuous" means that if x is close to a then f(x) is close to f(a). In a discrete topology, no two different points are ever close together.

So the only requirement for continuity is that, if two points x,a are close, i.e. if they are equal, then the values f(x) and f(a) should be close. That is pretty easy.

4. Aug 24, 2004