Applied General Topology - Vol 15, No 1 (2014)
URI permanente para esta colecciónhttps://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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Publicación 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.Publicación 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.Publicación 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.Publicación On the existence of best proximity points for generalized contractions(Editorial Universitat Politècnica de València, 2014-04-07) Sultana, Asrifa; Vetrivel, V.; University Grants Commission, India[EN] In this article we establish the existence of a unique best proximity point for some generalized non self contractions on a metric space in a simpler way using a geometric result. Our results generalize some recent best proximity point theorems and several fixed point theorems proved by various authors.Publicación 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.Publicación On topological groups via a-local functions(Editorial Universitat Politècnica de València, 2014-04-07) Al-Omeri, Wadei; Noorani, M. Salmi Md.; Al-Omari, A.; Ministry of Higher Education, Malasia[EN] An ideal on a set X is a nonempty collection of subsetsof X which satisfies the following conditions (1)A ∈ I and B ⊂ A implies B ∈ I; (2) A ∈ I and B ∈ I implies A ∪ B ∈ I. Given a topological space (X; ) an ideal I on X and A ⊂ X, ℜa(A) is defined as ∪{U ∈ a : U − A ∈ I}, where the family of all a-open sets of X forms a topology [5, 6], denoted by a. A topology, denoted a , finer than a is generated by the basis (I; ) = {V − I : V ∈ a(x); I ∈ I}, and a topology, denoted ⟨ℜa( )⟩ coarser than a is generated by the basis ℜa( ) = {ℜa(U) : U ∈ a}. In this paper A bijection f : (X; ; I) → (X; ;J ) is called a A∗-homeomorphism if f : (X; a ) → (Y; a ) is ahomeomorphism, ℜa-homeomorphism if f : (X;ℜa( )) → (Y;ℜa()) is a homeomorphism. Properties preserved by A∗-homeomorphism are studied as well as necessary and sufficient conditions for a ℜa-homeomorphism to be a A∗-homeomorphism.Publicación 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.Publicación Quadruple fixed point theorems for nonlinear contractions on partial metric spaces(Editorial Universitat Politècnica de València, 2014-04-07) Karapinar, Erdal; Tas, Kenan[EN] The notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapınar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.Publicación Hausdorff connectifications(Editorial Universitat Politècnica de València, 2014-04-07) Ramkumar, Solai[EN] Disconnectedness in topological space is analyzed to obtain Hausdorff connectifications of that topological space. Hausdorff connectifications are obtained by some direct constructions and by some partitions of connectifications. Also lattice structure is included in the collection of all Hausdorff connectifications.