A fixed point conjecture for Borsuk continuous set-valued mappings

被引：1

作者：

Miklaszewski, D ^{[1
]}

机构：

[1] Nicholas Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

FUNDAMENTA MATHEMATICAE | 2002年 / 175卷 / 01期

关键词：

set-valued mapping; fixed point; Borsuk continuity; bundle; characteristic class;

D O I：

10.4064/fm175-1-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main result of this paper is that for n = 3,4,5 and k = n - 2, every Borsuk continuous set-valued map of the closed ball in the n-dimensional Euclidean space with values which are one-point sets or sets homeomorphic to the k-sphere has a fixed point. Our approach fails for (k,n) = (1,4). A relevant counterexample (for the homological method, not for the fixed point conjecture) is indicated.

引用

页码：69 / 78

页数：10

共 29 条

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