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

[21] On the Brouwer fixed point theorem
Miklaszewski, D
[J]. TOPOLOGY AND ITS APPLICATIONS, 2002, 119 (01) : 53 - 64
[22] Miklaszewski D., 2001, TOPOL METHOD NONL AN, V17, P125
[23] O'Neil B., 1947, DUKE MATH J, V14, P689
[24] ON 3-MANIFOLDS WITH LOCAL SO(2) ACTION
ORLIK, P
RAYMOND, F
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1969, 20 (78) : 143 - &
[25] A FIXED-POINT INDEX FOR BIMAPS
SCHIRMER, H
[J]. FUNDAMENTA MATHEMATICAE, 1990, 134 (02) : 93 - 104
[26] Three dimensional topology of contained areas.
Seifert, H
[J]. ACTA MATHEMATICA, 1933, 60 (01) : 147 - 238
[27] SMALE S., 1959, P AM MATH SOC, V10, P621, DOI [10.2307/2033664, DOI 10.2307/2033664.T88]
[28] Steenrod N. E., 1962, Cohomology operations
[29] Switzer R.M., 1975, ALGEBRAIC TOPOLOGY H

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