
Olela Otafudu, Olivier
[EN] We introduce and investigate the concept of geodesic bicombing in T0quasimetric spaces. We prove that any Isbellconvex T0quasimetric space admits a geodesic bicombing which satisfies the equivariance property. Additionally, we show that many results on geodesic bicombing hold in quasimetric settings, provided that non symmetry in quasimetric spaces holds.

Yan, PengFei; Hu, XingYu; Xie, LiHong
[EN] In this paper, the concept of kupper semicontinuous setvalued mappings is introduced. Using this concept, we give characterizations of ksemistratifiable and kMCM spaces, which answers a question posed by Xie and Yan.

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

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.

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

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 polyhedraKawith simplicial bonding functions pba and X = lim X, then there exists a uniquely determined subinverse system XX= (La, pbaLb,(A,)) of X where for each a, La is a subcomplex of Ka, each pbaLb:Lb → La is...

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 ...

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 setopen 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 quasiuniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλclosedness and right UλKcompleteness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasiuniform...

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, 221238 (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.

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.

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

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 LiYorke is studied. At the end we give some examples to investigate the controlled shadowing property.

Boxer, Laurence
[EN] We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.

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.