Covering dimension using toric varieties

Abstract

In this paper we deduce the Lebesgue and the Knaster--Kuratowski--Mazurkiewicz theorems on the covering dimension, as well as their certain generalizations, from some simple facts of toric geometry. This provides a new point of view on this circle of results.

References in corpus (3)

• A topological central point theorem
• An analogue of Gromov's waist theorem for coloring the cube
• The genus and the Lyusternik-Schnirelmann category of preimages

Cited by in corpus (1)

• Colorful versions of the Lebesgue, KKM, and Hex theorem