Applied General Topology - Vol 05, No 2 (2004)

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  • A fuzzification of the category of M-valued L-topological spaces
  • On separation axioms of uniform bundles and sheaves
  • On the cardinality of indifference classes
  • Resolvability of ball structures
  • Relative Collectionwise Normality
  • Continuous representability of interval orders
  • Which topologies can have immediate successors in the lattice of T1-topologies?
  • Spaces whose Pseudocompact Subspaces are Closed Subsets
  • Two transfinite chains of separation conditions between T1 and T2

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    Two transfinite chains of separation conditions between T1 and T2
    (Universitat Politècnica de València, 2004-10-01) Sequeira, Luís
    [EN] Two new families of separation conditions have arisen in the study of the impact that the algebraic properties of topological algebras have on the topologies that may occur on their underlying spaces. We describe the relative strengths of these families of separation conditions for general spaces.
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    Spaces whose Pseudocompact Subspaces are Closed Subsets
    (Universitat Politècnica de València, 2004-10-01) Dow, Alan; Porter, Jack R.; Stephenson, R.M.; Grant Woods, R.; National Science Foundation, EEUU
    [EN] Every first countable pseudocompact Tychonoff space X has the property that every pseudocompact subspace of X is a closed subset of X (denoted herein by “FCC”). We study the property FCC and several closely related ones, and focus on the behavior of extension and other spaces which have one or more of these properties. Characterization, embedding and product theorems are obtained, and some examples are given which provide results such as the following. There exists a separable Moore space which has no regular, FCC extension space. There exists a compact Hausdorff Fréchet space which is not FCC. There exists a compact Hausdorff Fréchet space X such that X, but not X2, is FCC.
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    Which topologies can have immediate successors in the lattice of T1-topologies?
    (Universitat Politècnica de València, 2004-10-01) Alas, Ofelia T.; Wilson, Richard G.; Consejo Nacional de Ciencia y Tecnología, México
    [EN] We give a new characterization of those topologies which have an immediate successor or cover in the lattice of T1-topologies on a set and show that certain classes of compact and countably compact topologies do not have covers.
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    Continuous representability of interval orders
    (Universitat Politècnica de València, 2004-10-01) Candeal, Juan C.; Induráin, Esteban; Zudaire, M.; Ministerio de Educación y Cultura
    [EN] In the framework of the analysis of orderings whose associated indifference relation is not necessarily transitive, we study the structure of an interval order, and its representability through a pair of continuous real-valued functions. Inspired in recent characterizations of the representability of interval orders, we obtain new results concerning the existence of continuous real-valued representations. Classical results are also restated in a unified framework.
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    Relative Collectionwise Normality
    (Universitat Politècnica de València, 2004-10-01) Grabner, Eliser; Grabner, Gary; Miyazaki, Kazumi; Tartir, Jamal
    [EN] In this paper we study properties of relative collectionwise normality type based on relative properties of normality type introduced by Arhangel’skii and Genedi. Theorem Suppose Y is strongly regular in the space X. If Y is paracompact in X then Y is collectionwise normal in X. Example A T2 space X having a subspace which is 1− paracompact in X but not collectionwise normal in X. Theorem Suppose that Y is s- regular in the space X. If Y is metacompact in X and strongly collectionwise normal in X then Y is paracompact in X.