## Recursos de colección

#### RiuNet. Repositorio institucional de la Universitat de Valencia (86.722 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

1. #### 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....

2. #### 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

3. #### Sheaf cohomology on network codings: maxflow-mincut theorem

[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.

4. #### 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.

5. #### Oriented components and their separations

[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.

6. #### 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.

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

[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.

8. #### 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.

9. #### Generalized Normal Product Adjacency in Digital Topology

Boxer, Laurence
[EN] We study properties of Cartesian products of digital images for which adjacencies based on the normal product adjacency are used. We show that the use of such adjacencies lets us obtain many "product properties" for which the analogous statement is either unknown or invalid if, instead, we were to use c_u-adjacencies.

10. #### Generalized c-distance on cone b-metric spaces endowed with a graph and fixed point results

Fallahi, Kamal; Abbas, Mujahid; Soleimani Rad, Ghasem
[EN] The aim of this paper is to present fixed point results of contractive mappings in the framework of cone b-metric spaces endowed with a graph and associated with a generalized c-distance. Some corollaries and an example are presented to support the main result proved herein. Our results unify, extend and generalize various comparable results in the literature.

11. #### Convergence theorems for finding the split common null point in Banach spaces

Suantai, Suthep; Srisap, Kittipong; Naprang, Natthapong; Mamat, Manatsawin; Yundon, Vithoon; Cholamjiak, Prasit
[EN] In this paper, we introduce a new iterative scheme for solving the split common null point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.

12. #### An equivalence of results in C*-algebra valued b-metric and b-metric spaces

Dung, Nguyen Van; Le Hang, Vo Thi; Dolicanin-Djekic, Diana
[EN] In this paper, we first construct ab-metric, which is a special type ofC∗-algebra-valuedb-metrics, from a givenC∗-algebra-valuedb-metricand prove some equivalences between them. Then we show that notonly fixed point results but also topological properties inC∗-algebra-valuedb-metric spaces may be deduced from certain results inb-metricspaces. In particular, everyC∗-algebra-valuedb-metric space is metriz-able.

13. #### A study of function space topologies for multifunctions

Gupta, Ankit; Sarma, Ratna Dev
[EN] Function space topologies are investigated for the class ofcontinuousmultifunctions. Using the notion of continuous convergence, splitting-ness and admissibility are discussed for the topologies on continuousmultifunctions. The theory of net of sets is further developed for thispurpose. The(τ,μ)-topology on the class of continuous multifunctionsis found to be upper admissible, while the compact-open topology isupper splitting. The point-open topology is the coarsest topology whichis coordinately admissible, it is also the finest topology which is coor-dinately splitting.

14. #### A decomposition of normality via a generalization of $\kappa$-normality

Das, Ananga Kumar; Bhat, Pratibha
[EN] A simultaneous generalization of $\kappa$-normality and weak $\theta$-normality is introduced. Interrelation of this generalization of normality with existing variants of normality is studied.In the process of investigation a new decomposition of normality is obtained.

15. #### Unitary representability of free abelian topological groups

[EN] For every Tikhonov space X the free abelian topological group A(X) and the free locally convex vector space L(X) admit a topologically faithful unitary representation. For compact spaces X this is due to Jorge Galindo.

16. #### The Jordan curve theorem in the Khalimsky plane

Bouassida, Ezzeddine
[EN] The connectivity in Alexandroff topological spaces is equivalent to the path connectivity. This fact gets some specific properties to Z2, equipped with the Khalimsky topology. This allows a sufficiently precise description of the curves in Z2 and permit to prove a digital Jordan curve theorem in Z2.

Filali, Mahmoud; Protasov, Igor V.
[EN] A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant called the spread of a ballean. In particular, we show that, for every ordinal ballean B, spread of B coincides with density of B.

18. #### Semigroups and their topologies arising from Green's left quasiorder

Richmond, Bettina
[EN] Given a semigroup (S, ·), Green’s left quasiorder on S is given by a ≤ b if a = u · b for some u ϵ S1. We determine which topological spaces with five or fewer elements arise as the specialization topology from Green’s left quasiorder for an appropriate semigroup structure on the set. In the process, we exhibit semigroup structures that yield general classes of finite topological spaces, as well as general classes of topological spaces which cannot be derived from semigroup structures via Green’s left quasiorder.

19. #### Scott-representability of some spaces of Tall and Miskin

Bennet, Harold; Lutzer, David
[EN] In this paper we show that a variation of a technique of Miskin and Tall yields a cocompact completely regular Moore space that is Scott-domain-representable and has a closed Gδ-subspace that is not Scott-domain-representable. This clarifies the general topology of Scott-domain-representable spaces and raises additional questions about Scott-domain representability in Moore spaces.

20. #### Review of the book of Vladimir Kovalevsky "Geometry of Locally Finite Spaces"

Matveev, Sergei
No abstract.

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