Applied General Topology - Vol 04, No 2 (2003)

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https://riunet7pre.upv.es/handle/10251/82347

Tabla de contenidos



  • Multivalued function spaces and Atsuji spaces
  • Unusual and bijectively related manifolds
  • Transitivity of hereditarily metacompact spaces
  • Extensions of closure spaces
  • Quasi-pseudometric properties of the Nikodym-Saks space
  • Closure properties of function spaces
  • Locally convex approach spaces
  • A short note on hit-and-miss hyperspaces
  • A better framework for first countable spaces
  • Bounded point evaluations for cyclic Hilbert space operators
  • Five different proofs of extraresolvability of countable totally bounded groups
  • Groups with a small set of generators
  • Developable hyperspaces are metrizable
  • Orderability and continuous selections for Wijsman and Vietoris hyperspaces
  • Paths in hyperspaces
  • Hyperconvergences
  • Bombay hypertopologies
  • Graph topologies on closed multifunctions
  • n-Tuple relations and topologies on function spaces
  • A note on separation in AP
  • Some properties of the containing spaces and saturated classes of spaces
  • Density topology and pointwise convergence

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Now showing 1 - 5 of 22
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    Density topology and pointwise convergence
    (Universitat Politècnica de València, 2003-10-01) Wilczynski, Wladyslaw
    [EN] We shall show that the space of all approximately continuous functions with the topology of pointwise convergence is not homeomorphic to its category analogue.
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    Some properties of the containing spaces and saturated classes of spaces
    (Universitat Politècnica de València, 2003-10-01) Iliadis, Stavros
    [EN] Subjects of this paper are: (a) containing spaces constructed in [2] for an indexed collection S of subsets, (b) classes consisting of ordered pairs (Q,X), where Q is a subset of a space X, which are called classes of subsets, and (c) the notion of universality in such classes. We show that if T is a containing space constructed for an indexed collection S of spaces and for every X ϵ S, QX is a subset of X, then the corresponding containing space TIQ constructed for the indexed collection Q ={QX : X ϵ S} of spaces, under a simple condition, can be considered as a specific subset of T. We prove some “commutative” properties of these specific subsets. For classes of subsets we introduce the notion of a (properly) universal element and define the notion of a (complete) saturated class of subsets. Such a class is “saturated” by (properly) universal elements. We prove that the intersection of (complete) saturated classes of subsets is also a (complete) saturated class. We consider the following classes of subsets: (a) IP(Cl), (b) IP(Op), and (c) IP(n.dense) consisting of all pairs (Q;X) such that: (a) Q is a closed subset of X, (b) Q is an open subset of X, and (c) Q is a never dense subset of X, respectively. We prove that the classes IP(Cl) and IP(Op) are complete saturated and the class IP(n.dense) is saturated. Saturated classes of subsets are convenient to use for the construction of new saturated classes by the given ones.
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    A note on separation in AP
    (Universitat Politècnica de València, 2003-10-01) Lowen, R.; Sioen, M.
    [EN] It is our aim in this note to take a closer look at some separation axioms in the construct AP of approach spaces and contractions. Whereas lower separation axioms seem to be qualitative, the higher ones seem to have a quantitative nature. Also some characterizations for the corresponding epireectors will be given.
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    n-Tuple relations and topologies on function spaces
    (Universitat Politècnica de València, 2003-10-01) Georgiou, D.N.; Iliadis, S.D.; Papadopoulos, B.K.
    [EN] In some results concerning S-splitting, S-jointly continuous, D-splitting and D-jointly continuous topologies are considered, where S and D are the Sierpinski space and the double-point space, respectively. Here we generalize these results replacing the spaces S and D by any finite space.
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    Graph topologies on closed multifunctions
    (Universitat Politècnica de València, 2003-10-01) Di Maio, Giuseppe; Meccariello, Enrico; Naimpally, Somashekhar
    [EN] In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.