On a property of functions on a sphere
type: Item
instance of: scholarly article
title: On a property of functions on a sphere
zbMATH Open document ID: 1027.55005
DOI: 10.1023/A:1012922809398
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: The well-known Knaster conjecture claims the following: for any points \(w_1,\dots, w_k\in S^{k+m-2}\) and an arbitrary (continuous map) \(f: S^{k+m-2}\to \mathbb{R}^m\) there is a rotation \(A\in \text{SO}(k+m-1)\) of the sphere such that \(f(Aw_1)=\cdots= f(Aw_k)\). The author proves this conjecture for the case in which \(n= p^2\) for an odd prime \(p\) and the points lie on a circle and divide it into equal parts.
Mathematics Subject Classification ID: 55M35
zbMATH DE Number: 1927817
zbMATH Keywords: functions on a sphere
zbMATH Keywords: prime number
zbMATH Keywords: Knaster conjecture
author: Alexey Volovikov
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1012922809398
OpenAlex ID: W46549627
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description: scientific article; zbMATH DE number 1927817