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单词 LiftingTheorem
释义

lifting theorem


Let p:EB be a covering map and f:XB be a (continuousMathworldPlanetmath)map where X, B and E are path connected and locally path connected (http://planetmath.org/LocallyConnected).Also let xX and eE be points such that f(x)=p(e).Then f lifts to a map f~:XE with f~(x)=e if and only ifπ1(f) maps π1(X,x) inside the imageπ1(p)(π1(E,e)), where π1 denotes the fundamentalgroup functor. Furthermore f~ is unique (provided it exists of course).

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更新时间:2025/5/4 11:08:02