
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 selfdistance 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.

Aydi, Hassen; Abbas, Mujahid
[EN] In this paper, we introduce the concept of Wcompatiblity 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.

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.

Alas, Ofelia T.; MadrizMendoza, 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), 1119).

Morales López, Luis Felipe
[EN] A condensation is a onetoone 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!.

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 selfintersecting. These counterexamples were discovered using curve visualizing software and numerical algorithms that produce general procedures to create more examples.

Minguzzi, E.
[EN] A topological preordered space admits a Hausdorff T2preorder 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 T2preorder 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 T2preorder compactification is considered.

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.

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

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...

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

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.

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 nonuniform net will be treated....

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

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
maxflowmincut theorem with network coding sheaves in the case of multiple source.

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 quasiuniform convergence topologies U_{A} (A⊆P(X)) on F(X,Y) and their comparison in the setting of Y a quasiuniform space. Further, we study U_{A}closedness and right Kcompleteness properties of certain subspaces of generalized continuous functions in F(X,Y) in the case of Y a locally symmetric quasiuniform space or a locally uniform space.

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.

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, 275286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.

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.

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 Ntopological 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 Ntopological spaces and discuss the relationships between them.