Question: need help with this (b) Suppose X is a compact topological space. Prove that for any equivalence relation ~ on X , the quotient space

need help with this

(b) Suppose X is a compact topological space. Prove that for any equivalence relation ~ on X , the quotient space X / N is compact. (c) Fix an equivalence relation ~ on a topological space X. Suppose that f : X > Y is a continuous map with the property that if 3: ~ 3', then f (56) = f (93")- (i) Construct a function f\" : X / ~> Y so that f' o q = f. (ii) Prove that f' is continuous

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