Search

In this paper, we define and study the notions of normal∗ and w-anchored dicovers as important classes of covers, convenient for the texture theory. Especially, a ditopological counterpart is given for the well-known result that in a completely regular topological space, the collection of all normal covers forms a uniformity compatible with the topology. In addition, we describe two kinds of dicovers called divisible and even, in order to characterize the largest di-uniformity on textures, as well as characterizing the full dinormality which is introduced by L.M. Brown and M. Diker (Paracompactness and full normality in ditopological texture spaces, J. Math. Annal. Appl.227 (1998), 144–165). [ABSTRACT FROM AUTHOR]

In this paper we continue previous investigations on the weaker forms of the Menger property in bitopological spaces. We introduce weakly Menger property and study some topological properties of almost and weakly Menger bitopological spaces. We also consider the almost Hurewicz spaces in a bitopological context. [ABSTRACT FROM AUTHOR]

We continue our study of selection principles in texture and ditopological texture spaces began in [14] . Our focus here is on the Hurewicz covering properties in texture structures and direlational uniform texture spaces. The behavior of these properties under standard operations with ditopological spaces are considered. We give game-theoretic and Ramsey-theoretic characterizations of the Hurewicz property in texture spaces, and establish relationships between selection properties of di-uniform spaces and (quasi-) uniform spaces. [ABSTRACT FROM AUTHOR]

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies. [ABSTRACT FROM AUTHOR]

We study selective versions of separability in bitopological spaces by using the notions of θ -closure and θ -density. Additionally, we consider games associated to these selection properties. [ABSTRACT FROM AUTHOR]

Abstract: The authors characterize di-uniformities on a texture in the sense of Özçağ and Brown (Di-uniform texture spaces, Appl. Gen. Top. 4(1) (2003), 157–192) in terms of functions on the texturing . This characterization enables quasi-uniformities in the sense of Hutton (Uniformities on Fuzzy Topological Spaces, J. Math. Anal. Appl. 58 (1977) 559–571) to be regarded as di-uniformities on the corresponding Hutton Texture, thereby revealing di-uniformities as a generalization of Hutton quasi-uniformities. The effect of imposing a complementation on is also considered and several important results established. [Copyright &y& Elsevier]

Abstract: We study selective versions of separability in bitopological spaces. In particular, we investigate these properties in function spaces endowed with the topology of pointwise convergence and the compact-open topology. [Copyright &y& Elsevier]

Abstract: The author introduces the notions of Lebesgue di-uniformity and co Lebesgue di-uniformity and investigates the relationship between a Lebesgue quasi uniformity on X and the corresponding Lebesgue di-uniformity on the discrete texture . Finally a notion of a dual dicovering Lebesgue quasi di-uniform texture space is introduced and several properties are discussed. [Copyright &y& Elsevier]

The present paper is concerned with the Alexandroff one point compactification of the Marcus-Wyse (M-, for brevity) topological space (Z 2 , γ) . This compactification is called the infinite M-topological sphere and denoted by ((Z 2) ∗ , γ ∗) , where (Z 2) ∗ : = Z 2 ∪ { ∗ } , ∗ ∉ Z 2 and γ ∗ is the topology for (Z 2) ∗ induced by the topology γ on Z 2 . With the topological space ((Z 2) ∗ , γ ∗) , since any open set containing the point " ∗ " has the cardinality ℵ 0 , we call ((Z 2) ∗ , γ ∗) the infinite M-topological sphere. Indeed, in the fields of digital or computational topology or applied analysis, there is an unsolved problem as follows: Under what category does ((Z 2) ∗ , γ ∗) have the fixed point property (FPP, for short)? The present paper proves that ((Z 2) ∗ , γ ∗) has the FPP in the category M o p (γ ∗) whose object is the only ((Z 2) ∗ , γ ∗) and morphisms are all continuous self-maps g of ((Z 2) ∗ , γ ∗) such that | g ((Z 2) ∗) | = ℵ 0 with ∗ ∈ g ((Z 2) ∗) or g ((Z 2) ∗) is a singleton. Since ((Z 2) ∗ , γ ∗) can be a model for a digital sphere derived from the M-topological space (Z 2 , γ) , it can play a crucial role in topology, digital geometry and applied sciences. [ABSTRACT FROM AUTHOR]