“Antipodal”的概念、定义、习题解题方法及翻译-数学辞典

单词	Antipodal
释义	antipodal DefinitionSuppose $x$ and $y$ are points on the $n$ -sphere (http://planetmath.org/Sphere) $S^{n}$ .If $x=-y$ then $x$ and $y$ are called antipodal points. Theantipodal map is the map $A:S^{n}\\to S^{n}$ defined as $A(x)=-x$ . Properties 1. The antipodal map $A:S^{n}\\to S^{n}$ ishomotopic (http://planetmath.org/HomotopyOfMaps)to the identity map if $n$ is odd [1]. 2. The degree (http://planetmath.org/DegreeMapOfSpheres) of theantipodal map is $(-1)^{n+1}$ . References 1 V. Guillemin, A. Pollack,Differential topology, Prentice-Hall Inc., 1974.
随便看	proof of Chinese remainder theorem ProofOfChoquetsCapacitabilityTheorem proof of Choquet’s capacitability theorem ProofOfChromaticNumberAndGirth proof of chromatic number and girth ProofOfClarksonInequality proof of Clarkson inequality ProofOfClassEquationTheorem proof of class equation theorem ProofOfClassificationOfSeparableHilbertSpaces proof of classification of separable Hilbert spaces ProofOfClosedCurveTheorem proof of closed curve theorem ProofOfClosedDifferentialFormsOnASimpleConnectedDomain proof of closed differential forms on a simple connected domain ProofOfClosedGraphTheorem proof of closed graph theorem ProofOfCofactorExpansion proof of cofactor expansion ProofOfCompactnessTheoremForFirstOrderLogic proof of compactness theorem for first order logic ProofOfCompactPavingsAreClosedSubsetsOfACompactSpace proof of compact pavings are closed subsets of a compact space ProofOfComparisonTest proof of comparison test

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。

antipodal

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