Hi there, I've got quite a big assignment about topological spaces and think I'm doing OK apart from this bit...

Let X and Y be topological spaces. Show that is continuous if and only if

. By considering the map , show that we

do not expect .

For the first part I know, f is continuous if and only if the image of the closure of every subset is contained in the closure of the image which implies the result but don't think this is really me showing this, its just me stating a rule...

For second part I'd have thought we would expect soI'm obviously not understanding something properly.

Any help much appreciated!!