Applied General Topology - Vol 05, No 1 (2004)

Permanent URI for this collection

https://riunet7pre.upv.es/handle/10251/82540

Tabla de contenidos



  • Iterated starcompact topological spaces
  • Representations of ordered semigroups and the Physical concept of Entropy
  • The topological structure of (homogeneous) spaces and groups with countable cs∗-character
  • A topological approach to Best Approximation Theory
  • Some problems on selections for hyperspace topologies
  • Star-Hurewicz and related properties
  • Homeomorphisms of R and the Davey Space
  • A countably compact free Abelian group whose size has countable cofinality
  • Continuous functions with compact support
  • Partial metrizability in value quantales
  • Fuzzy quasi-metric spaces

Browse

Recent Submissions

Now showing 1 - 5 of 11
  • Thumbnail Image
    Publication
    Fuzzy quasi-metric spaces
    (Universitat Politècnica de València, 2004-04-01) Gregori, Valentín; Romaguera, Salvador; Generalitat Valenciana
    [EN] We generalize the notions of fuzzy metric by Kramosil and Michalek, and by George and Veeramani to the quasi-metric setting.We show that every quasi-metric induces a fuzzy quasi-metric and ,conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. Other basic properties are discussed.
  • Thumbnail Image
    Publication
    Partial metrizability in value quantales
    (Universitat Politècnica de València, 2004-04-01) Kopperman, Ralph D.; Matthews, S.; Pajoohesh, H.; Engineering and Physical Sciences Research Council, Reino Unido; UK Research and Innovation; City University of New York
    [EN] Partial metrics are metrics except that the distance from a point to itself need not be 0. These are useful in modelling partially defined information, which often appears in computer science. We generalize this notion to study “partial metrics” whose values lie in a value quantale which may be other than the reals. Then each topology arises from such a generalized metric, and for each continuous poset, there is such a generalized metric whose topology is the Scott topology, and whose dual topology is the lower topology. These are both corollaries to our result that a bitopological space is pairwise completely regular if and only if there is such a generalized metric whose topology is the first topology, and whose dual topology is the second.
  • Thumbnail Image
    Publication
    Continuous functions with compact support
    (Universitat Politècnica de València, 2004-04-01) Acharyya, Sudip Kumar; Chattopadhyaya, K.C.; Ghosh, Partha Pratim
    [EN] The main aim of this paper is to investigate a subring of the ring of continuous functions on a topological space X with values in a linearly ordered field F equipped with its order topology, namely the ring of continuous functions with compact support. Unless X is compact, these rings are commutative rings without unity. However, unlike many other commutative rings without unity, these rings turn out to have some nice properties, essentially in determining the property of X being locally compact non-compact or the property of X being nowhere locally compact. Also, one can associate with these rings a topological space resembling the structure space of a commutative ring with unity, such that the classical Banach Stone Theorem can be generalized to the case when the range field is that of the reals.
  • Thumbnail Image
    Publication
    A countably compact free Abelian group whose size has countable cofinality
    (Universitat Politècnica de València, 2004-04-01) Castro Pereira, I.; Tomita, A.H.; Ministry of Education, Culture, Sports, Science and Technology, Japón
    [EN] Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “k-Lindelöfness” and ”k-compactness” for cardinals k. To focus only hit-and-miss structures, could look quite old-fashioned, but some importance, at least for the techniques, is given by a recent result of Som Naimpally, to who this article is hearty dedicated.
  • Thumbnail Image
    Publication
    Homeomorphisms of R and the Davey Space
    (Universitat Politècnica de València, 2004-04-01) Carter, Sheila; Craveiro de Carvalho, F.J.
    [EN] Up to homeomorphism, there are 9 topologies on a three point set {a, b, c}. Among the resulting topological spaces we have the so called Davey space, where the only non-trivial open set is, let us say, {a}. This is an interesting topological space to the extent that every topological space can be embedded in a product of Davey spaces. In this note we will consider the problem of obtaining the Davey space as a quotient R/G, where G is a suitable homeomorphism group. The present work can be regarded as a follow-up to some previous work done by one of the authors and Bernd Wegner.