Good Coverings of Proximal Alexandrov Spaces. Homotopic Cycles in Jordan Curve Theorem Extension

2021/08/10 by James F. Peters, J. F. Peters, Peters, J. F. +3
Computer Science · Mathematics · #54E05 #55P57 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GT #msc:54E05 #msc:55P57

paper · pdf · doi:10.48550/arxiv.2108.10113

19 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2104.05601

arxiv created 2021/08/10 · openalex publication_date 2021/08/10 · arxiv updated 2021/08/24 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

This paper introduces proximal homotopic cycles, which lead to the main results in this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning Theorem with different forms of Tanaka good cover of an Alexandrov space equipped with a proximity relation and extensions of the Jordan curve theorem. An application of these results is also given.

Citations

• Good Coverings of Proximal Alexandrov Spaces. Path Cycles in the Extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems

Related

• Good Coverings of Proximal Alexandrov Spaces. Path Cycles in the Extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems
• Good coverings of Alexandrov spaces
• Lipschitz homotopy convergence of Alexandrov spaces
• A Short Study of Alexandroff Spaces
• Regular coverings and fundamental groupoids of Alexandroff spaces