On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space

被引：0

作者：

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

机构：

[1] Voronezh State Univ, Voronezh, Russia

[2] Peoples Friendship Univ Russia, Moscow, Russia

来源：

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2019年 / 53卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

surjective operator; contraction mapping; Lipschitz constant; topological dimension;

D O I：

10.1007/s10688-019-0249-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The solvability of the equation A(x) = f(x) on the sphere of a Hilbert space and the dimension of its solution set are studied in the case where A is a closed surjective operator and f is an odd Lipschitz mapping. A kind of analogue of the infinite-dimensional version of the Borsuk-Ulam theorem is obtained.

引用

页码：61 / 64

页数：4

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