Covering dimension using toric varieties

2013/07/12 by Роман Карасев, Roman Karasev · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AT #math.MG #msc:14M25 #msc:52B20 #msc:54F45 #msc:55M10 #msc:55M30

paper · pdf · doi:10.1016/j.topol.2014.08.006

published as Topology and its Applications 177 (2014), 59-65

arxiv created 2013/07/12 · openalex publication_date 2014/08/29 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Using the Borsuk–Ulam Theorem

Cited by

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

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