Applied General Topology - Vol 15, No 1 (2014)

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https://riunet.upv.es/handle/10251/43522

Tabla de contenidos

Hausdorff connectifications
Quadruple fixed point theorems for nonlinear contractions on partial metric spaces
Near metrizability via a new approach
On topological groups via a-local functions
On some properties of $T_0$-ordered reflection
On the existence of best proximity points for generalized contractions
Unified common fixed point theorems under weak reciprocal continuity or without continuity
Baire spaces and hyperspace topologies revisited
Soft set theory and topology

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Now showing 1 - 5 of 7

Soft set theory and topology
(Editorial Universitat Politècnica de València, 2014-04-07) Georgiou, D. N.; Megaritis, A. C.
[EN] In this paper we study and discuss the soft set theory giving new definitions, examples, new classes of soft sets, and properties for mappings between different classes of soft sets. Furthermore, we investigate the theory of soft topological spaces and we present new definitions, characterizations, and properties concerning the soft closure, the soft interior, the soft boundary, the soft continuity, the soft open and closed maps, and the soft homeomorphism.
Baire spaces and hyperspace topologies revisited
(Editorial Universitat Politècnica de València, 2014-04-07) Bourquin, Steven; Zsilinszky, Laszlo
[EN] It is the purpose of this paper to show how to use approach spaces to get a unified method of proving Baireness of various hyperspace topologies. This generalizes results spread in the literature including the general (proximal) hit-and-miss topologies, as well as various topologies generated by gap and excess functionals. It is also shown that the Vietoris hyperspace can be non-Baire even if the base space is a 2nd countable Hausdorff Baire space.
Unified common fixed point theorems under weak reciprocal continuity or without continuity
(Editorial Universitat Politècnica de València, 2014-04-07) Kadelburg, Zoran; Imdad, Mohammad; Chauhan, Sunny
[EN] The purpose of this paper is two fold. Firstly, using the notion of weak reciprocal continuity due to Pant et al. Weak reciprocal continuity and fixed point theorems, Ann. Univ. Ferrara Sez. VII Sci. Mat. 57(1), 181-190 (2011)], we prove unified common fixed point theorems for various variants of compatible and $R$-weakly commuting mappings in complete metric spaces employing an implicit relation which covers a multitude of contraction conditions yielding thereby known as well as unknown results as corollaries. Secondly, we point out that more natural results can be proved under relatively tighter conditions if we replace the completeness of the space by completeness of suitable subspaces. The realized improvements in our results are also substantiated using appropriate examples.
On some properties of T0−ordered reflection
(Editorial Universitat Politècnica de València, 2014-04-07) Lazaar, Sami; Mhemdi, Abdelouaheb
[EN] In [12], the authors give an explicit construction of the T0−ordered reflection of an ordered topological space (X, τ,≤) . All ordered topological spaces such that whose T0−ordered reflections are T1−ordered spaces are characterized. In this paper, some properties of the T0−ordered reflection of a given ordered topological space (X, τ,≤) are studies. The class of morphisms in ORDTOP orthogonal to all T0−ordered topological space is characterized.
Near metrizability via a new approach
(Editorial Universitat Politècnica de València, 2014-04-07) Mandal, Dhananjoy; Mukherjee, M. N.; University Grants Commission, India
[EN] The present article deals with near metrizability, initiated in an earlier paper, with a new orientation and approach. The notions of nearly regular and uniform pseudo-bases are introduced and analogues of some results concerning metrizability and paracompactness are obtained for near metrizability and near paracompactness respectively via the proposed approach, suitably formulated.

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