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RiuNet. Repositorio institucional de la Universitat de Valencia (101.684 recursos)

RiuNet es el Repositorio Institucional de la Universitat Politècnica de València, gestionado por la Biblioteca, cuyo objetivo es ofrecer acceso en Internet a la producción científica, académica y corporativa de la comunidad universitaria con la finalidad de aumentar su visibilidad y hacerla accesible y preservable.

Applied General Topology

Mostrando recursos 1 - 20 de 165

  1. More on ultrafilters and topological games

    González-Silva, R.A.; Hrusák, M.
    [EN] Two different open-point games are studied here, the G-game and the Gp-game, defined for each p ∈ ω∗. We prove that for each p ∈ ω∗, there exists a space in which none of the players of the Gp-game has a winning strategy.Nevertheless a result of P. Nyikos, essentially shows that it is consistent, that there exists a countable space in which all these games are undetermined.We construct a countably compact space in which player II of the Gp-game is the winner, for every p ∈ ω∗. With the same technique of construction we built a countably compact space...

  2. Well-posedness, bornologies, and the structure of metric spaces

    Beer, Gerald; Segura, Manuel
    [EN] Given a continuous nonnegative functional λ that makes sense defined on an arbitrary metric space (X, d), one may consider those spaces in which each sequence (xn) for which lim n→∞λ(xn) = 0 clusters. The compact metric spaces, the complete metric spaces, the cofinally complete metric spaces, and the UC-spaces all arise in this way. Starting with a general continuous nonnegative functional λ defined on (X, d), we study the bornology Bλ of all subsets A of X on which limn→∞λ(an) = 0 ⇒ (an) clusters, treating the possibility X ∈ Bλ as a special case. We characterize those...

  3. Topologies on function spaces and hyperspaces

    Georgiou, D.N.
    [EN] Let Y and Z be two fixed topological spaces, O(Z) the family of all open subsets of Z, C(Y,Z) the set of all continuous maps from Y to Z, and OZ(Y ) the set {f−1(U) : f ϵ C(Y,Z) and U ϵ O(Z)}. In this paper, we give and study new topologies on the sets C(Y,Z) and OZ(Y ) calling (A,A0)-splitting and (A,A0)-admissible, where A and A0 families of spaces.

  4. Pointwise convergence and Ascoli theorems for nearness spaces

    Yang, Zhanbo
    [EN] We first study subspaces and product spaces in the context of nearness spaces and prove that U-N spaces, C-N spaces, PN spaces and totally bounded nearness spaces are nearness hereditary; T-N spaces and compact nearness spaces are N-closed hereditary. We prove that N2 plus compact implies N-closed subsets. We prove that totally bounded, compact and N2 are productive. We generalize the concepts of neighborhood systems into the nearness spaces and prove that the nearness neighborhood systems are consistent with existing concepts of neighborhood systems in topological spaces, uniform spaces and proximity spaces respectively when considered in the respective sub-categories....

  5. F-supercontinuous functions

    Kohli, J.K.; Singh, D.; Aggarwal, Jeetendra
    [EN] A strong variant of continuity called ‘F-supercontinuity’ is introduced. The class of F-supercontinuous functions strictly contains the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33 (7) (2002), 1097–1108) which in turn properly contains the class of cl-supercontinuous functions ( clopen maps) (Appl. Gen. Topology 8 (2) (2007), 293–300; Indian J. Pure Appl. Math. 14 (6) (1983), 762–772). Further, the class of F-supercontinuous functions is properly contained in the class of R-supercontinuous functions which in turn is strictly contained in the class of continuous functions. Basic properties of F-supercontinuous functions are studied and their place in the hierarchy...

  6. Embedding into discretely absolutely star-Lindelöf spaces II

    Song, Yan-Kui
    [EN] A space X is discretely absolutely star-Lindelöf if for every open cover U of X and every dense subset D of X, there exists a countable subset F of D such that F is discrete closed in X and St(F, U) = X, where St(F, U) = S{U ∈ U : U ∩F 6= Ø}. We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed G-subspace.

  7. Condensations of Cp(X) onto σ-compact spaces

    Tkachuk, Vladimir V.
    [EN] We show, in particular, that if nw(Nt) ≤ k for any t ϵ T and C is a dense subspace of the product ǁ{Nt : t 2 T} then, for any continuous (not necessarily surjective) map ϕ : C ͢ K of C into a compact space K with t(K) ≤ k, we have ψ(ϕ (C)) ≤ k. This result has several applications in Cp-theory. We prove, among other things, that if K is a non-metrizable Corson compact space then Cp(K) cannot be condensed onto a σ-compact space. This answers two questions published by Arhangel’skii and Pavlov.

  8. Best proximity pair theorems for relatively nonexpansive mappings

    Sankar Raj, V.; Veeramani, P.
    [EN] Let A, B be nonempty closed bounded convex subsets of a uniformly convex Banach space and T : A∪B → A∪B be a map such that T(A) ⊆ B, T(B) ⊆ A and ǁTx − Tyǁ ≤ ǁx − yǁ, for x in A and y in B. The fixed point equation Tx = x does not possess a solution when A ∩ B = Ø. In such a situation it is natural to explore to find an element x0 in A satisfying ǁx0 − Tx0ǁ = inf{ǁa − bǁ : a ∈ A, b ∈ B} = dist(A,B)....

  9. Some aspects of Isbell-convex quasi-metric spaces

    Olela Otafudu, Olivier
    [EN] We introduce and investigate the concept of geodesic bicombing in T0-quasi-metric spaces. We prove that any Isbell-convex T0-quasi-metric space admits a geodesic bicombing which satisfies the equivariance property. Additionally, we show that many results on geodesic bicombing hold in quasi-metric settings, provided that non symmetry in quasi-metric spaces holds.

  10. k-semistratifiable spaces and expansions of set-valued mappings

    Yan, Peng-Fei; Hu, Xing-Yu; Xie, Li-Hong
    [EN] In this paper, the concept of k-upper semi-continuous set-valued mappings is introduced. Using this concept, we give characterizations of k-semistratifiable and k-MCM spaces, which answers a question posed by Xie and Yan.

  11. Fixed point theorems for nonlinear contractions with applications to iterated function systems

    Pant, Rajendra
    [EN] We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an application to iterated function systems.

  12. Few remarks on maximal pseudocompactness

    Bella, Angelo
    [EN] A pseudocompact space is maximal pseudocompact if every strictly finer topology is no longer pseudocompact. The main result here is a counterexample which answers a question rised by Alas, Sanchis and Wilson.

  13. Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence

    Jäger, Gunther; Ahsanullah, T. M. G.
    [EN] We identify two categories of quantale-valued convergence tower spaces that are isomorphic to the categories of quantale-valued metric spaces and quantale-valued partial metric spaces, respectively. As an application we state a quantale-valued metrization theorem for quantale-valued convergence tower groups.

  14. Topological n-cells and Hilbert cubes in inverse limits

    Rubin, Leonard R.
    [EN] It has been shown by S. Mardešić that if a compact metrizable space X has dim X ≥ 1 and X is the inverse limit of an inverse sequence of compact triangulated polyhedra with simplicial bonding maps, then X must contain an arc. We are going to prove that if X = (|Ka|,pba,(A,))is an inverse system in set theory of triangulated polyhedra|Ka|with simplicial bonding functions pba and X = lim X, then there exists a uniquely determined sub-inverse system XX= (|La|, pba|Lb|,(A,)) of X where for each a, La is a subcomplex of Ka, each pba|Lb|:|Lb| → |La| is...

  15. Some categorical aspects of the inverse limits in ditopological context

    Yildiz, Filiz
    [EN] This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category ifPDitop, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category InvifPDitop consisting of the inverse systems constructed by the objects and morphisms of ifPDitop, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems -...

  16. Set-open topologies on function spaces

    Alqurashi, Wafa Khalaf; Khan, Liaqat Ali; Osipov, Alexander V.
    [EN] Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform...

  17. Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions

    Ahmadullah, Md; Imdad, Mohammad; Arif, Mohammad
    [EN] In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))] and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper.

  18. Partially topological group action

    Al Shumrani, M. A.
    [EN] The concept of partially topological group was recently introduced in [3]. In this article, we define partially topological group action on partially topological space and we generalize some fundamental results from topological group action theory.

  19. Counting coarse subsets of a countable group

    Protasov, Igor; Protasova, Ksenia
    [EN] For every countable group G, there are 2ω distinct classes of coarselyequivalent subsets of G.

  20. Controlled shadowing property

    Zamani Bahabadi, Alireza
    [EN] In this paper we introduce a new notion, named controlled shadowing property and we relate it to some notions in dynamical systems such as topological ergodicity, topologically mixing and specication properties. The relation between the controlled shadowing and chaos in sense of Li-Yorke is studied. At the end we give some examples to investigate the controlled shadowing property.

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