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?