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单词 ClassificationOfCoveringSpaces
释义

classification of covering spaces


Let X be a connectedPlanetmathPlanetmath, locally path connected and semilocally simplyconnected space. Assume furthermore that X has a basepoint *.

A covering p:EX is called based if E is endowed with abasepoint e and p(e)=*. Two based coverings pi:EiX, i=1,2 are calledequivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath if there is a basepoint preserving equivalence T:E1E2 thatcovers the identityPlanetmathPlanetmath, i.e. T is a homeomorphism and the following diagramcommutes

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更新时间:2025/5/4 22:55:09