Question: Suppose that c X and that f : E Y. a) Prove that f is continuous on E if and only if f-l

Suppose that £ c X and that f : E → Y.
a) Prove that f is continuous on E if and only if f-l (A) n £ is relatively closed in £ for all closed sets A in Y.
b) Suppose that f is continuous on E. Prove that if V is relatively open in f(E), then f-1(V) is relatively open in E, and if A is relatively closed in f(E), then f-1(A) is relatively closed in £.

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