A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps

被引：1

作者：

Gel'man, B. D. ^{[1
,2
]}

机构：

[1] Voronezh State Univ, Moscow, Russia

[2] Russian Univ Peoples Friendship, Moscow, Russia

来源：

SBORNIK MATHEMATICS | 2016年 / 207卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

multivalued map; Borsuk-Ulam theorem; surjective operator; level set of a function; topological dimension; FIXED-POINTS;

D O I：

10.1070/SM8588

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to the proof of the infinite-dimensional Borsuk-Ulam theorem for odd completely continuous multivalued maps with convex images which are defined on level sets of even functions. The results obtained in the paper are new even for single-valued maps. In the final section some applications of the theorem to analysis and differential equations are discussed.

引用

页码：841 / 853

页数：13

共 50 条

[31] The Borsuk-Ulam theorem for general spaces
Pergher, PLQ
De Mattos, D
Dos Santos, EL
[J]. ARCHIV DER MATHEMATIK, 2003, 81 (01) : 96 - 102
[32] THE BORSUK-ULAM THEOREM AND BISECTION OF NECKLACES
ALON, N
WEST, DB
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 98 (04) : 623 - 628
[33] ON A BORSUK-ULAM THEOREM FOR STIEFEL MANIFOLDS
YOKOYAMA, O
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1995, 71 (02) : 33 - 34
[34] SOME GENERALIZATIONS OF BORSUK-ULAM THEOREM
NUSSBAUM, RD
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1977, 35 (JUL) : 136 - 158
[35] NONSYMMETRIC GENERALIZATION OF BORSUK-ULAM THEOREM
JOSHI, KD
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (01): : A212 - &
[36] EQUIVALENT FORMULATIONS OF BORSUK-ULAM THEOREM
BACON, P
[J]. CANADIAN JOURNAL OF MATHEMATICS, 1966, 18 (03): : 492 - &
[37] The Borsuk-Ulam theorem for general spaces
P. L. Q. Pergher
D. de Mattos
E. L. dos Santos
[J]. Archiv der Mathematik, 2003, 81 : 96 - 102
[38] COINCIDENCE THEOREM RELATED TO BORSUK-ULAM THEOREM
COHEN, F
CONNETT, JE
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (01) : 218 - 220
[39] Geometric proofs of the two-dimensional Borsuk-Ulam theorem
Siburg K.F.
[J]. Mathematische Semesterberichte, 2009, 56 (1) : 79 - 84
[40] The Borsuk-Ulam Theorem for n-valued maps between surfaces
Vinicius Casteluber Laass
Carolina de Miranda e Pereiro
[J]. Geometriae Dedicata, 2024, 218

← 1 2 3 4 5 →