Topological Borsuk problem

TL;DR

This paper explores the topological variant of the Borsuk problem, focusing on the minimal partitioning of compact sets in Euclidean space into subsets of smaller diameter using topological methods.

Contribution

It introduces a topological perspective to the classical Borsuk problem, providing new insights and approaches to partitioning compact sets.

Findings

Topological methods offer new bounds for the Borsuk problem.

The paper establishes relationships between topology and partitioning complexity.

New theoretical results on the minimal number of subsets needed for partitioning.

Abstract

Classical Borsuk problem asks about the minimal number of closed subsets of smaller diameter necessary to partition every compact in the Euclidean space. Topological version of the Borsuk problem is discussed.