publication . Preprint . 2015

Strong Proximities on Smooth Manifolds and Vorono\" i Diagrams

Peters, J. F.; Guadagni, C.;
Open Access English
  • Published: 13 Jun 2015
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.
arXiv: Mathematics::Symplectic GeometryMathematics::Differential GeometryMathematics::Geometric Topology
free text keywords: Mathematics - General Topology, 54E05 (Primary), 57N16 (Secondary)
Funded by
  • Funder: Natural Sciences and Engineering Research Council of Canada (NSERC)
Download from
52 references, page 1 of 4

[1] G. Beer, A. Di Concilio, G. Di Maio, S. Naimpally, C.M. Pareek, J.F. Peters, Somashekhar Naimpally, 1931-2014, Topology and its Applications 188 (2015), 97-109.

[2] G. Beer, Topologies on Closed and Closed Convex Sets, Mathematics and its Applications, 268. Kluwer Academic Publishers Group, Dordrecht, (1993), xii+340 pp. ISBN: 0-7923-2531- 1, MR1269778.

[3] G. Beer, R.K. Tamaki, On hit-and-miss hyperspace topologies, Comment. Math. Univ. Carolin. 34 (1993), no. 4, 717728, MR1263801.

[4] E. C˘ech, Topological Spaces, Publishing House of the Czechoslovak Academy of Sciences, Prague; Interscience Publishers John Wiley & Sons Ltd., London, UK, 1966, from seminar, Brno, 1936-1939; rev. ed. Z. Frol´ık, M. Kat˘etov, 893 pp, MR0211373.

[5] A. Di Concilio, Uniformities, hyperspaces, and normality, Monatsh. Math. 107 (1989), no. 3, 303-308, MR1012462.

[6] A. Di Concilio, Action on hyperspaces, Topology Proc. 41 (2013), 85-98, MR2923735.

[7] A. Di Concilio, Proximity: a powerful tool in extension theory, function spaces, hyperspaces, boolean algebra and point-set topology, F. Mynard and E. Pearl(eds), Beyond Topology, Contemporary Mathematics Amer. Math. Soc.,486, (2009), 89-114.

[8] A. Di Concilio, S.A. Naimpally, Proximal set-open topologies, Boll. Unione Mat. Ital. Sez. B Artic Ric. Mat. 8 (2000), no. 1, 173-191, MR1755708.

[9] A. Di Concilio, Proximal set-open topologies on partial maps, Acta Math. Hungar. 88 (2000), no. 3, 227-237, MR1767801.

[10] A. Di Concilio, Point-free geometries: Proximities and quasi-metrics, Math. in Comp. Sci. 7 (2013), no. 1, 31-42, MR3043916.

[11] G. Di Maio, Lj.D.R. Ko˘cinac, Some covering properties of hyperspaces, Topology Appl. 155 (2008), no. 17-18, 19591969, MR2457978.

[12] G. Di Maio, L. Hol´a, On hit-and-miss topologies, Rendiconto dell'Accademia delle Scienze Fisiche e Matematiche (4) LXII (1995), 103-124, MR1419286.

[13] G. Di Maio, S.A. Naimpally, Comparison of hypertopologies, Rend. Istit. Mat. Univ. Trieste 22 (1992), no. 1-2, 140-161, MR1210485.

[14] G.L. Dirichlet, U¨ber die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen, Journal fu¨r die reine und angewandte Math. 40 (1850), 221-239.

[15] H. Edelsbrunner, A Short Course in Computational Geometry and Topology, Springer, Berlin, 110 pp.

52 references, page 1 of 4
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue