Question: Problem 10. Suppose that two topological space X and Y are homeomorphic. 1. If X is metrizable, show that Y is also metrizable. (In particular,

Problem 10. Suppose that two topological space X and Y are homeomorphic. 1. If X is metrizable, show that Y is also metrizable. (In particular, a metrizable space and a non-metrizable space cannot be homeomorphic.) 2. Explain why (R, 7Euc) and (R, Teof ) are not homeomorphic

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