Let X be a compact space, and Y a space. Let f: X Y be a surjective continuous function. Show that Y is compact. (note: It's done in the book, so you may copy the proof used in the book. Or you can solve it yourself.) Hint for Problem 2. Let (Uafael be an open cover of Y. Consider the family {f-¹(Ua)}a€1 of subsets of X. Show that it's an open cover of X, and use it somehow. You may prove and use the fact f(f-¹(A)) = A, for any subset A of Y (you need surjectivity of f).