Covering dimension using toric varieties

TL;DR

This paper offers a novel perspective on covering dimension theorems by deriving classical results from principles in toric geometry, linking topological dimension theory with algebraic geometry.

Contribution

It introduces a new approach to covering dimension theorems using toric varieties, connecting topology with algebraic geometry.

Findings

Derived Lebesgue and KKM theorems from toric geometry principles

Generalized classical covering dimension results using algebraic geometric methods

Provided a new conceptual framework for understanding covering dimension

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.