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
收藏
页码：61 / 64
页数：4
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