publication . Preprint . 2015

Strong Proximities on Smooth Manifolds and Vorono\" i Diagrams

Peters, J. F.; Guadagni, C.;
Open Access English
  • Published: 13 Jun 2015
Abstract
This article introduces strongly near smooth manifolds. The main results are (i) second countability of the strongly hit and far-miss topology on a family $\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to which singletons are added, (ii) manifold strong proximity, (iii) strong proximity of charts in manifold atlases implies that the charts have nonempty intersection. The application of these results is given in terms of the nearness of atlases and charts of proximal manifolds and what are known as Vorono\" i manifolds.
Subjects
arXiv: Mathematics::Symplectic GeometryMathematics::Differential GeometryMathematics::Geometric Topology
free text keywords: Mathematics - General Topology, 54E05 (Primary), 57N16 (Secondary)
Funded by
NSERC
Project
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
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