1. If f:X-->Y is a homeomorphism, the f(Cl(A)) = Cl(f(A)) for every 2. If f:X-->Y is a homeomorphism, the f( (A)) = for every
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Originally Posted by r2dee6 1. If f:X-->Y is a homeomorphism, the f(Cl(A)) = Cl(f(A)) for every 2. If f:X-->Y is a homeomorphism, the f( (A)) = for every Lemma 1. Let be a function on the indicated topological spaces. f is continuous iff for each subset A of X, . (1) Since is continuous, by lemma 1. We know that is also continuous. Thus, by lemma 1. We have . We conclude that . (2) Since f is a homeomorphism, .
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