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.
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.
[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.; 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).
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!.
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.
[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.
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.
[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.