Strong Proximities on Smooth Manifolds and Vorono\" i Diagrams

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Peters, J. F.; Guadagni, C.;
  • Subject: 54E05 (Primary), 57N16 (Secondary) | Mathematics - General Topology
    arxiv: Mathematics::Differential Geometry | Mathematics::Geometric Topology | Mathematics::Symplectic Geometry

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) man... View more
  • References (52)
    52 references, page 1 of 6

    [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.

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