Hi,

i just learned the notions of jointly and separately cont. functions.

A function f: X x Y -> A is called

1) jointly cont <=> f is cont. w.r.t. the product topology

2) separ. cont <=> f and are cont.

So i tryed to show 1) => 2).

But all my attempts failed.

Can you help me?

One of my attemts:

Let be cont. then we get an open set ., whereas X' and Y' are open in X, Y respectively.

If we now consider the map and take some U \subset A.

Now we have to proof, is open in Y. But why is this correct in all top. spaces?

Regards