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| ``Why is inclusion map a topological embedding?''
by zhaoway on 2003-11-23 09:32:47 |
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| I read in John M. Lee's book: Introduction to topological manifolds, proposition 3.4 (a) says that inclusion map is a topological embedding. But let's suppose there is an inclusion map from a closed subset A of X to X, then in the subspace of A inherited from X, A itself is an open set, while its image after the inclusion map is a closed subset in X. Henceforthly, this inclusion map between A and its image is not a homeomorphism. Hence no topological embedding. Where have I gone wrong? Please! Thank you!
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