Suborbits in Knaster's problem

Abstract

In this paper we exhibit a similarity between Euclidean Ramsey problems and Knaster-type problems. By borrowing ideas from Ramsey theory we prove weak Knaster properties of non-equatorial triangles in spheres, and of simplices in Euclidean spaces.

Minor corrections are made after reviewing in the journal

References in corpus (2)

• Dvoretzky type theorems for multivariate polynomials and sections of convex bodies
• Topological aspects of the Dvoretzky Theorem