1. The problem statement, all variables and given/known data 1. If A and B are closed. Show that A x B is a closed subset of X x Y with the product topology. 2. Give an example of a closed subset W of RxR such that the first component of W (it is made up of two components) is not closed in R. For 2. How does one recognise a closed subset W in RxR? For 1. How do you show A x B is closed in general? Is the only way from functions like pi and when one end is open or closed the other must be as well.