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单词 Pathwise-Connected
释义

Pathwise-Connected

A Topological Space is pathwise-connected Iff for every two points , there is a ContinuousFunction 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 andCW-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.

See also Connected Space, CW-Complex, Locally Pathwise-Connected Space, Topological Space
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更新时间:2025/4/3 16:14:26