I'm sorry if this should be in the Analysis forum; I figured it pertained to topology though. Let Y be a subspace of a metric space (X,d) and let A be a subset of Y. The proposition includes conditions for A to be open or closed in Y. In class the teacher first proved when A is open and then used complements to prove when A is closed. I'm trying to go the other way around and prove the case when A is closed first, using the sequence criterion. The statement is: A is closed in Y iff there is a closed set C in X such that [tex]A=C \cap Y[/tex] I haven't really used the sequential criterion for closed sets before, so I don't really know where to start :/ can you provide a starting point? Do I need to construct C or can I abstractly prove the existence of one?