[SOLVED] Path-connected subspaces

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• July 2nd 2008, 04:53 PM
Catherine Morland
[SOLVED] Path-connected subspaces
Is it true that every topological space is the disjoint union of path-connected subspaces?
• July 3rd 2008, 06:02 AM
algebraic topology
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.