Is it true that every topological space is the disjoint union of path-connected subspaces?

Printable View

- Jul 2nd 2008, 03:53 PMCatherine Morland[SOLVED] Path-connected subspaces
Is it true that every topological space is the disjoint union of path-connected subspaces?

- Jul 3rd 2008, 05:02 AMalgebraic topology
Define a relation ~ on topological space

*X*by $\displaystyle a\sim b\iff$ 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*.