i want so solve this exercise, but i don't know how?:
"X,Y metric spaces, Y locally compact. F C(X,Y).
f is proper iff is compact for all K
proper means in our definition, that forall top. spaces Z:
f x id_z: X x Z->Y x Z is closed.
How can i proof this thm.?`
i try a lot of things, but i can't solve this problem.
i hope, you can help me by hints..