Could someone help me prove the following:
Let be a continuos map between metric-spaces and . Prove that if is a pathwise connected subset in , then the image under is a pathwise connected subset in .
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is surjective so, for there exist such that and . As is pathwise connected, there exists a path from to contained in . Then, is a path from to contained in . Fernando Revilla
Last edited by FernandoRevilla; Jan 12th 2011 at 04:08 AM.
Originally Posted by FernandoRevilla is surjective By the way surjective, I suppose you understand why is surjective .
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