Applied General Topology - Vol 17, No 1 (2016)

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https://riunet.upv.es/handle/10251/72348

Tabla de contenidos



  • The equivalence of two definitions of sequential pseudocompactness
  • A uniform approach to normality for topological spaces
  • Convergence in graded ditopological texture spaces
  • A local fixed point theorem for set-valued mappings on partial metric spaces
  • On topological groups with remainder of character k
  • Two classes of metric spaces
  • Normally preordered spaces and continuous multi-utilities

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    Two classes of metric spaces
    (Universitat Politècnica de València, 2016-04-12) Garrido, Isabel; Meroño, Ana S.; Ministerio de Economía y Competitividad
    [EN] The class of metric spaces (X,d) known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.
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    The equivalence of two definitions of sequential pseudocompactness
    (Universitat Politècnica de València, 2016-04-12) Lipparini, Paolo
    We show that two possible definitions of sequential pseudocompactness are equivalent, and point out some consequences.[EN]
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    On topological groups with remainder of character k
    (Universitat Politècnica de València, 2016-04-12) Bonanzinga, Maddalena; Cuzzupè, Maria Vittoria
    [EN] In [A.V. Arhangel'skii and J. van Mill, On topological groups with a first-countable remainder, Top. Proc. 42 (2013), 157-163] it is proved that the character of a non-locally compact topological group with a first countable remainder doesn't exceed $\omega_1$ and a non-locally compact topological group of character $\omega_1$ having a compactification whose reminder is first countable is given. We generalize these results in the general case of an arbitrary infinite cardinal k. 
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    Normally preordered spaces and continuous multi-utilities
    (Universitat Politècnica de València, 2016-04-12) Bosi, Gianni; Caterino, Alessandro; Ceppitelli, Rita
    [EN] We study regular, normal and perfectly normal preorders by referring to suitable assumptions concerning the preorder and the topology of the space. We also present conditions for the existence of a countable continuous multi-utility representation, hence a Richter-Peleg multi-utility representation, by assuming the existence of a countable net weight.
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    Convergence in graded ditopological texture spaces
    (Universitat Politècnica de València, 2016-04-12) Ekmekçi, Ramazan; Ertürk, Rıza
    [EN] Graded ditopological texture spaces have been presented and discussed in categorical aspects by Lawrence M. Brown and Alexander Sostak (see bibliography). In this paper, the authors generalize the structure of difilters in ditopological texture spaces defined in (see bibliography) to the graded ditopological texture spaces and compare the properties of difilters and graded difilters.