SOLVED: Question 4. [10 5 Points] Let X,Y be topological spaces.A continuous map f X-Y is a local homeomorphism if for every e X there exists a neighborhood U C X of x,such that f(Uis open in Yand f:U-f(U defined by Jr=f(x is a homeomorphism. Let Tx be the topology on X and Ty the topology on Y. a Suppose that f is a surjective local homeomorphism. Show that the topology Ty of Y equals the set S=fU|UeTx It can be shown that any covering map is a local homeomorphism. Recall that pR-S defined by

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