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On the Borsuk-Ulam Theorem for Lipschitz Mappings on an Infinite-Dimensional Space
Functional Analysis and Its Applications ( IF 0.6 ) Pub Date : 2019-06-01 , DOI: 10.1007/s10688-019-0249-4
B. D. Gel’man

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.

中文翻译:

无限维空间上Lipschitz映射的Borsuk-Ulam定理

A是封闭的射影算子且f是奇数Lipschitz映射的情况下,研究了方程Ax)= fx)在希尔伯特空间球面上的可解性及其解集的维数。获得了Borsuk-Ulam定理的无穷维形式的一种类似物。
更新日期:2019-06-01
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