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

[1] An infinite-dimensional version of the Borsuk-Ulam theorem
Gel'man, BD
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2004, 38 (04) : 239 - 242
[2] An infinite-dimensional version of the Borsuk-Ulam theorem
B. D. Gel’man
[J]. Functional Analysis and Its Applications, 2004, 38 : 239 - 242
[3] Borsuk-Ulam theorem in infinite-dimensional Banach spaces
Gel'man, BD
[J]. SBORNIK MATHEMATICS, 2002, 193 (1-2) : 83 - 91
[4] On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space
Gel'man, B. D.
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2019, 53 (01) : 61 - 64
[5] On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space
B. D. Gel’man
[J]. Functional Analysis and Its Applications, 2019, 53 : 61 - 64
[6] A CONTINUOUS VERSION OF THE BORSUK-ULAM THEOREM
JAWOROWSKI, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 82 (01) : 112 - 114
[7] Borsuk-Ulam type theorems for multivalued maps
Singh, Hemant Kumar
Singh, Konthoujam Somorjit
[J]. HIROSHIMA MATHEMATICAL JOURNAL, 2022, 52 (03) : 321 - 331
[8] A parametrized version of the Borsuk-Ulam theorem
Schick, Thomas
Simon, Robert Samuel
Spiez, Stanislaw
Torunczyk, Henryk
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2011, 43 : 1035 - 1047
[9] A HOMOLOGY VERSION OF THE BORSUK-ULAM THEOREM
WALKER, JW
[J]. AMERICAN MATHEMATICAL MONTHLY, 1983, 90 (07): : 466 - 468
[10] The Borsuk-Ulam theorem for maps into a surface
Goncalves, Daciberg Lima
Guaschi, John
[J]. TOPOLOGY AND ITS APPLICATIONS, 2010, 157 (10-11) : 1742 - 1759

← 1 2 3 4 5 →