A Topological Space is pathwise-connected Iff for every two points , there is a Continuous Function from [0,1] to such that and . Roughly speaking, a Space is pathwise-connected if, for every two points in , there is a path connecting them. For Locally Pathwise-Connected Spaces (which include most ``interesting spaces'' such as Manifolds and CW-Complexes), being Connected and being pathwise-connected are equivalent, although there are connected spaces which are not pathwise connected. Pathwise-connected spaces are also called 0-connected.

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1999-05-26