Equivalence of Planar Čech Nerves and Complexes
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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.
KeywordsBall Čech complex Čech nerve Cover Homotopic equivalence
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