National Academy Science Letters

, Volume 42, Issue 6, pp 529–530 | Cite as

Equivalence of Planar Čech Nerves and Complexes

  • J. F. Peters
  • H. DuttaEmail author
Short Communication


This article introduces proximal Čech nerves and Čech complexes, restricted to finite, bounded regions K of the Euclidean plane. A Čech nerve is a collection of intersecting balls. A main result of this article is extension of the Edelsbrunner–Harer Nerve Theorem for Čech nerves and Čech complexes.


Ball Čech complex Čech nerve Cover Homotopic equivalence 



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Copyright information

© The National Academy of Sciences, India 2019

Authors and Affiliations

  1. 1.Computational Intelligence LaboratoryUniversity of ManitobaWinnipegCanada
  2. 2.Department of Mathematics, Faculty of Arts and SciencesAdiyaman UniversityAdiyamanTurkey
  3. 3.Department of MathematicsGauhati UniversityGuwahatiIndia

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