This exercise is used many times from Section 10.5 onward. Let Y be a subspace of X.

Question:

This exercise is used many times from Section 10.5 onward. Let Y be a subspace of X.
a) Show that a set V is open in Y if and only if there is an open set U in X such that V = U C\Y.
b) Show that a set £ is closed in Y if and only if there is a closed set A in X such that £ = A n K.