Applied General Topology - Vol 15, No 2 (2014)

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https://riunet.upv.es/handle/10251/43608

Tabla de contenidos



  • New common fixed point theorems for multivalued maps
  • Convergence S-compactifications
  • Asymptotic structures of cardinals
  • The classical ring of quotients of $C_c(X)$
  • R-spaces and closedness/completeness of certain function spaces in the topology of uniform convergence
  • On the topology of the chain recurrent set of a dynamical system
  • Lifting Dynamical Properties to Hyperspaces
  • Function lattices and compactifications
  • Computational topology for approximations of knots
  • Approximation in different smoothness spaces with the RAFU method
  • Radicals in the class of compact right topological rings
  • Subgroups of paratopological groups and feebly compact groups

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    Subgroups of paratopological groups and feebly compact groups
    (Editorial Universitat Politècnica de València, 2014-10-01) Fernández, Manuel; Tkachenko, Mikhail G.; Consejo Nacional de Ciencia y Tecnología, México
    [EN] It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method of refining the topology of a given commutative paratopological group G such that the group G with the finer topology, say, σ is again a paratopological group containing a subgroup whose closure in (G, σ) is not a subgroup. It is also proved that a feebly compact paratopological group H is perfectly k-normal and that every Gδ-dense subspace of H is feebly compact.
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    Radicals in the class of compact right topological rings
    (Editorial Universitat Politècnica de València, 2014-10-01) Ursul, Mihail; Tripe, Adela
    [EN] We construct in this article three radicals in the class of compact right topological rings. We prove also that a simple left Noetherian compact right topological ring is finite.
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    Approximation in different smoothness spaces with the RAFU method
    (Editorial Universitat Politècnica de València, 2014-10-01) Corbacho Cortés, Eduardo
    [EN] The RAFU method is an original and unknown approximation procedure we can use in Approximation Theory. We know that the RAFU method provides a linear space uniformly dense in C[a,b] by using some separation conditions. In this work, we will show we can employ the RAFU method to approximate functions of C0(R) and C00(R), Riemann integrable functions, Lebesgue integrable functions, functions of Lp[a,b] and Lp(R), 1≤p<¥ and measurable functions. Moreover, Riemann integrals can be approximated by the integrals of the functions that the RAFU method provides.
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    Computational topology for approximations of knots
    (Editorial Universitat Politècnica de València, 2014-10-01) Li, Ji; Peters, T. J.; Jordan, K. E.; National Science Foundation, EEUU; International Business Machines Corporation
    [EN] The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding:Hausdorff distance, anda sum of total curvature and derivative.High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. Subdivision can produce PL approximations for a given B\'ezier curve, fulfilling the above two conditions. The primary contributions are:       (i) a priori bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\'ezier curve, and       (ii) improved iteration bounds over those previously established. 
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    Function lattices and compactifications
    (Editorial Universitat Politècnica de València, 2014-10-01) Alaste, Tomi Matias
    [EN] Let F be a lattice of real-valued functions on a non-empty set X such that F contains the constant functions. Using certain filters on X determined by F, we construct a compact Hausdorff topological space δX with the property that every bounded member of F extends to δX and these extensions form a dense subspace of C(δX). If A is any C*-subalgebra of ℓ∞(X) containing the constant functions, then our construction gives a representation of the spectrum of A as a space of filters on X.