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RiuNet. Repositorio institucional de la Universitat de Valencia (94.443 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 51

  1. Weak partial metric spaces and some fixed point results

    Altun, Ishak; Durmaz, Gonca
    [EN] The concept of partial metric p on a nonempty set X was introduced by Matthews. One of the most interesting properties of a partial metric is that p(x, x) may not be zero for x e X. Also, each partial metric p on a nonempty set X generates a T0 topology on X. By omitting the small self-distance axiom of partial metric, Heckmann defined the weak partial metric space. In the present paper, we give some fixed point results on weak partial metric spaces.

  2. Tripled coincidence and fixed point results in partial metric spaces

    Aydi, Hassen; Abbas, Mujahid
    [EN] In this paper, we introduce the concept of W-compatiblity of mappings F : X × X × X ! X and g : X ! X and based on this notion, we obtain tripled coincidence and common tripled fixed point results in the setting of partial metric spaces. The presented results generalize and extend several well known comparable results in the existing literature. We also provide an example to support our results.

  3. Supersymmetry and the Hopf fibration

    Davis, Simon
    [EN] The Serre spectral sequence of the Hopf fibration S15 S7→S8 is computed. It is used in a study of supersymmetry and actions based on this fibration.

  4. Correction to: Some results and examples concerning Whyburn spaces

    Alas, Ofelia T.; Madriz-Mendoza, Maira; Wilson, Richard G.
    [EN] We correct the proof of Theorem 2.9 of the paper mentioned in the title (published in Applied General Topology, 13 No.1 (2012), 11-19).

  5. Continuous isomorphisms onto separable groups

    Morales López, Luis Felipe
    [EN] A condensation is a one-to-one continuous function onto. We give sufficient conditions for a Tychonoff space to admit a condensation onto a separable dense subspace of the Tychonoff cube Ic and discuss the differences that arise when we deal with topological groups, where condensation is understood as a continuous isomorphism. We also show that every Abelian group G with |G| 2c admits a separable, precompact, Hausdorff group topology, where c = 2!.

  6. Computational Topology Counterexamples with 3D Visualization of Bézier Curves

    Li, J.; Peters, T.J.; Marsh, D.; Jordan, K.E.
    [EN] For applications in computing, Bézier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R3 and yields a smooth polynomial curve C embedded in R3. It is of interest to understand when L and C have the same embeddings. One class ofc ounterexamples is shown for L being unknotted, while C is knotted. Another class of counterexamples is created where L is equilateral and simple, while C is self-intersecting. These counterexamples were discovered using curve visualizing software and numerical algorithms that produce general procedures to create more examples.

  7. Compactification of closed preordered spaces

    Minguzzi, E.
    [EN] A topological preordered space admits a Hausdorff T2-preorder compactification if and only if it is Tychonoff and the preorder is represented by the family of continuous isotone functions. We construct the largest Hausdorff T2-preorder compactification for these spaces and clarify its relation with Nachbin’s compactification. Under local compactness the problem of the existence and identification of the smallest Hausdorff T2-preorder compactification is considered.

  8. Common fixed points for generalized (v,o)-weak contractions in ordered cone metric spaces

    Nashine, Hemant Kumar; Aydi, Hassen
    [EN] The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized (v,o)-weak contractions in partially ordered cone metric spaces. Also, some illustrative examples are presented.

  9. Classification of separately continuous mappings with values in o-metrizable spaces

    Karlova, Olena
    [EN] We prove that every vertically nearly separately continuous mapping defined on a product of a strong PP-space and a topological space and with values in a strongly o-metrizable space with a special stratification, is a pointwise limit of continuous mappings.

  10. Core compactness and diagonality in spaces of open sets

    Jordan, Francis; Mynard, Frédéric
    [EN] We investigate when the space OX of open subsets of a topological space X endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of X, which in turn is characterized in terms of coincidence of the Scott topology of OX × OX with the product of the Scott topologies of OX at (X,X). On the other hand, we characterize diagonality of OX endowed with the Scott convergence and show that this space can be diagonal without being pretopological. New examples are provided to clarify the relationship between pretopologicity, topologicity and diagonality...

  11. A Kuratowski-Mrówka type characterization of fibrewise compactness

    Neira U.; Clara M.
    [EN] In this paper a Kuratowski-Mrówka type characterization of fibrewisecompact topological spaces is presented.

  12. Convergence semigroup categories

    Richardson, Gary; Mikusinski, Piotr; Boustique, H.
    [EN] Properties of the category consisting of all objects of the form (X, S, λ) are investigated, where X is a convergence space, S is a commutative semigroup, and λ: X × S → X is a continuous action. A “generalized quotient” of each object is defined without making the usual assumption that for each fixed g ∈ S, λ(., g) : X → X is an injection.

  13. Uniform reconstruction of continuous functions with the RAFU method

    Corbacho Cortés, Eduardo
    [EN] The RAFU (radical functions) method can be used to obtain the uniformreconstruction of a continuous function from its values at some ofthe points of partitions of a closed interval. In this work we willprove that we can reconstruct a continuous function from average samplesof these points, from linear combinations of them and from local averagesamples given by convolution. Uniform error bounds will be established. If these data are unknown but approximate values of them are known, uniform reconstruction will be also possible. Error estimates in these cases will be given. The case of a non-uniform net will be treated....

  14. Some fixed point theorems on non-convex sets

    Radhakrishnan, Mohanasundaram; Rajesh, S.; Agrawal, Sushama
    [EN] In this paper, we prove that ifKis a nonempty weakly compact setin a Banach spaceX,T:K→Kis a nonexpansive map satisfyingx+Tx2∈Kfor allx∈Kand ifXis3−uniformly convex orXhas theOpial property, thenThas a fixed point in K

  15. Sheaf cohomology on network codings: maxflow-mincut theorem

    Nguemo, Miradain Atontsa; Tcheka, Calvin
    [EN] Surveying briefly a novel algebraic topological application sheaf theory into directed network coding problems, we obtain the weak duality in multiple source scenario by using the idea of modified graph. Furthermore,we establish the maxflow-mincut theorem with network coding sheaves in the case of multiple source.

  16. Quasi-uniform convergence topologies on function spaces- Revisited

    Alqurash, Wafa Khalaf; Khan, Liaqat Ali
    [EN] Let X and Y be topological space and F(X,Y) the set of all functions from X into Y. We study various quasi-uniform convergence topologies U_{A} (A⊆P(X)) on F(X,Y) and their comparison in the setting of Y a quasi-uniform space. Further, we study U_{A}-closedness and right K-completeness properties of certain subspaces of generalized continuous functions in F(X,Y) in the case of Y a locally symmetric quasi-uniform space or a locally uniform space.

  17. Oriented components and their separations

    Stadler, Baerbel M R; Stadler, Peter F.
    [EN] There is a tight connection between connectedness, connected components, and certain types of separation spaces. Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches. Here, we introduce production relations as a further generalization of connectivity spaces and reaches and derive associated systems of oriented components that generalize connected components in a natural manner. The main result is a characterization of generalized reaches in terms of equivalent separation spaces.

  18. Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance

    Choban, Mitrofan M; Berinde, Vasile
    [EN] We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.

  19. Improved F-contraction of rational type on partial metric spaces

    Nazam, Muhammad; Arshad, Muhammad; Abbas, Mujahid
    [EN] Following the approach of $F$- contraction introduced by Wardowski \cite{DW}, in this paper, we introduce improved $F$-contraction of rational type in the framework of partial metric spaces and used it to obtain a common fixed point theorem for a pair of self mappings. We show, through example, that improved $F$-contraction is more general than $F$- contraction and guarantees fixed points in those cases where $F$-contraction fails to provide. Moreover, we apply this fixed point result to show the existence of common solution of the system of integral equations.

  20. Generalized open sets in grill N-topology

    Thivagar, M. Lellis; Reilly, Ivan L; Dasan, M. Arockia; Ramesh, V.
    [EN] The aim of this paper is to give a systematic development of grill N-topological spaces and discuss a few properties of local function. We build a topology for the corresponding grill by using the local function. Furthermore, we investigate the properties of weak forms of open sets in the grill N-topological spaces and discuss the relationships between them.

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