Applied General Topology - Vol 01, No 1 (2000)

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https://riunet7pre.upv.es/handle/10251/81885

Tabla de contenidos



  • Merotopies associated with quasi-uniformities
  • An operation on topological spaces
  • Some properties of o-bounded and strictly o-bounded groups
  • Extension properties and the Niemytzki plane
  • Useful topologies and separable systems
  • Jungck theorem for triangular maps and related results
  • Separation axioms in topological preordered spaces and the existence of continuous order-preserving functions
  • Preservation of completeness under mappings in asymmetric topology
  • Fuzzy functions: a fuzzy extension of the category SET and some related categories


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Recent Submissions

Now showing 1 - 5 of 10
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    On domains witnessing increase in information
    (Universitat Politècnica de València, 2000-10-01) Spreen, Dieter
    [EN] The paper considers algebraic directed-complete partial orders with a semi-regular Scott topology, called regular domains. As is well know, the category of Scott domains and continuous maps is Cartesian closed. This is no longer true, if the domains are required to be regular. Two Cartesian closed subcategories of the regular Scott domains are exhibited: regular dI-domains with stable maps and strongly regular Scott domains with continuous maps. Here a Scott domains is strongly regular if all of its compact open subsets are regular open. In one considers only embeddings of dependent products and sums. Moreover, they are w-cocomplete and their object classes are closed under several constructions used in programming language semantics. It follows that recursive domains equations can be solved and models of typed and untyped lambda calculi can be constructed. Both kinds of domains can be udes in giving meaning to programming language constructs.
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    Fuzzy functions: a fuzzy extension of the category SET and some related categories
    (Universitat Politècnica de València, 2000-10-01) Höhle, Ulrich; Porst, Hans-E.; Sostak, Alexander P.
    [EN] In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.
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    Preservation of completeness under mappings in asymmetric topology
    (Universitat Politècnica de València, 2000-10-01) Künzi, Hans-Peter A.; Swiss National Science Foundation
    [EN] The preservation of various completeness properties in the quasi-metric (and quasi-uniform) setting under open, closed and uniformly open mappings is investigated. In particular, it is noted that between quasi-uniform spaces the property that each costable filter has a cluster point is preserved under uniformly open continuous surjections. Furthermore in the realm of quasi-uniform spaces conditions under which almost uniformly open mappings are uniformly open are given which generalize corresponding classical results for uniform spaces. As a by-product it is shown that a quasi-metrizable Moore space admits a left K-complete quasi-metric if and only if it is a complete Aronszajn space.
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    Separation axioms in topological preordered spaces and the existence of continuous order-preserving functions
    (Universitat Politècnica de València, 2000-10-01) Bosi, Gianni; Isler, R.
    [EN] We characterize the existence of a real continuous order-preserving function on a topological preordered space, under the hypotheses that the topological space is normal and the preorder satisfies a strong continuity assumption, called IC-continuity. Under the same continuity assumption concerning the preorder, we present a sufficient condition for the existence of a continuous order-preserving function in case that the topological space is completely regular.
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    Jungck theorem for triangular maps and related results
    (Universitat Politècnica de València, 2000-10-01) Grinc, M.; Snoha, L.; State Committee for Scientific Research, Polonia; Slovak Research and Development Agency
    [EN] We prove that a continuous triangular map G of the n-dimensional cube In has only fixed points and no other periodic points if and only if G has a common fixed point with every continuous triangular map F that is nontrivially compatible with G. This is an analog of Jungck theorem for maps of a real compact interval. We also discuss possible extensions of Jungck theorem, Jachymski theorem and some related results to more general spaces. In particular, the spaces with the fixed point property and the complete invariance property are considered.