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Math Help - [SOLVED] Path-connected subspaces

  1. #1
    Newbie Catherine Morland's Avatar
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    [SOLVED] Path-connected subspaces

    Is it true that every topological space is the disjoint union of path-connected subspaces?
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  2. #2
    Junior Member
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    Define a relation ~ on topological space X by a\sim b\iff there exists a path from a to b in X. Then ~ is an equivalence relation on X and each equivalence class is a path-connected subspace of X.
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