张增喜.与某种拓广的Borsuk—UIam定理等价的几个命题[J].数学研究及应用,1992,12(3):339~344
与某种拓广的Borsuk—UIam定理等价的几个命题
A Generalized Borsuk-Ulam Theorem which is Equivalent to Some Propositions
投稿时间:1990-10-09  
DOI:10.3770/j.issn:1000-341X.1992.03.002
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作者单位
张增喜 北京师范学院分院数学系 
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中文摘要:
      
英文摘要:
      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.
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