16,441 research outputs found

    Stratified fibrations and the intersection homology of the regular neighborhoods of bottom strata

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    In this paper, we develop Leray-Serre-type spectral sequences to compute the intersection homology of the regular neighborhood and deleted regular neighborhood of the bottom stratum of a stratified PL-pseudomanifold. The E^2 terms of the spectral sequences are given by the homology of the bottom stratum with a local coefficient system whose stalks consist of the intersection homology modules of the link of this stratum (or the cone on this link). In the course of this program, we establish the properties of stratified fibrations over unfiltered base spaces and of their mapping cylinders. We also prove a folk theorem concerning the stratum-preserving homotopy invariance of intersection homology.Comment: To appear in Topology and Its Applications; see also http://www.math.yale.edu/~friedman

    Pretopological and topological lattice-valued convergence spaces

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    We show that the classical axiom which characterizes pretopological convergence spaces splits into two axioms in the general Heyting algebra-valued case. Furthermore we present a generalization of Kowalski’s diagonal condition to the lattice-valued case

    A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces

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    We study a category of lattice-valued uniform convergence spaces where the lattice is enriched by two algebraic operations. This general setting allows us to view the category of lattice-valued uniform spaces as a reflective subcategory of our category, and the category of probabilistic uniform limit spaces as a coreflective subcategory

    Lattice-valued convergence spaces and regularity

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    We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a continuous mapping from a subspace to a regular space. A characterization in the restricted case that the lattice is a complete Boolean algebra in terms of the closure of an L-filter is given

    Lattice-valued continuous convergence is induced by a lattice-valued uniform convergence structure

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    We define a stratified L-uniform convergence structure on the set of all continuous mappings from a stratified L-limit space to a stratified L-uniform convergence space. This structure induces L-continuous convergence. This shows that the category of all L-limit-uniformizable spaces is cartesian closed

    Compactification of lattice-valued convergence spaces

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    We define compactness for stratified lattice-valued convergence spaces and show that a Tychonoff theorem is true. Further a generalization of the classical Richardson compactification is given. This compactification has a universal property

    Initial Characterized L-spaces and Characterized L- topological Groups

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    In this research work, new topological notions are proposed and investigated. The notions are named initial characterized L-spaces and characterized L-topological groups. The properties of such notions are deeply studied. We show that the intitial characterized L-space for an characterized L-spaces exists. By this notion, the notions of characterized L-subspace and characterized product L-space are introduced and studied. More information can be found in the full paper
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