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In this paper, we prove a generalized form of Borsuk-Ulam theorem: Generalized Borsuk-Ulam Theorem Let (X, T) be T-space, where X is a n-dimensional homology sphere over the group T2 of integers mod 2, T is a topological transformation on X weth period 2 and hasn't any fixed points; f: X (?) Rn is any con-tinuous map from X into n-euclidean space Rn then, there existe at least a pair (X, T(X)) of involution points of some x ∈ X mapping into one point, i.e. f(X) = f(T(X)). In addition, we show that it is equivalent to some propositions too. 相似文献
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张增喜 《数学的实践与认识》2004,34(9):127-129
定义了复射动力系统以及它们之间等变映射的概念 ,在此基础上又引出了自相似集之间等变映射的概念并讨论了在此类映射的映射下自相似集象的 Hausdorff维数的状态 . 相似文献
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§0.序言及主要结果的陈述 在1947年,B.Knaster曾提出下列推测: 给定从(m n-2)-维的球面S~(m n-2)到m-维欧氏空间R~m的连续映射f:S~(m n-2)→R~m以及n个不同的点e_1,…,e_n∈S~(m n-2),是否存在一个旋转r,使得f(re_1)=…=f(re_n)? 对于这一问题已有不少人研究过:例如, 当m=1,n=3 且e_1,e_2,e_3(作为向量)互相垂直时,Kakutani给出了证明(我们称之为Kakutani定理)…。 相似文献
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TheSufficientandNecessaryConditionsfortheSpaceXin-Space(X,)tobeaCohomologySphereZhangZengxi(张增喜)(DepartmentofMathematics,Ca... 相似文献
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In[1j,theautherdefinedtheconceptof"specialindex"bythetoolthatissingularcohomologywithSmith-periodictransformationforarc-connectedHausdorffspaces.ThisconceptplaysacrucialroleinthestudyofB.Knasterconjecture.Inthispaper,wefirstdefinetheconceptof"specialsingularindex"corresp0ndingtothe"specialindex"byCech-cohomologywithSmithperi0dictransformationfor'X-compactconnectedHausd0rffspaces(seetheendof51..))andintroducetheconceptsofgr-map,X-homotopiesbetween.r-maps,X-homot0py-equivalentsbetweenx-space… 相似文献
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对T-空间之间引进了T-映射,T-同胚,T-映射的T-同伦,T-空间的T-同伦等价等概念.对T-紧致连通Hausdorff空间应用Cech-smith特异上同调理论定义了特异指数的概念,并在此基础上证明了T-空间的特异指数是T-空间的T-伦型不变量,从而也证明了它是T-空间的T-同胚不变量. 相似文献