This is the third of three papers which develop various fundamental aspects of the theory of ditopological texture spaces and relate this work with the theory of fuzzy topological spaces. In this paper, the authors define and study basic separation axioms in general ditopological texture spaces, relating these to known separation axioms for bitopological and topological spaces, and to the point...

Topological extensions are closely related to nearness structures of various kinds. For example, the Smirnov compactification of a proximity space X is a compact Hausdorff space Y which contains X as a dense subspace and for which it is true that a pair of subsets of X is near if, and only if, their closures in Y meet. Lodato generalized this result to weaker conditions for the proximity and th...

We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabili...

Dynamic topological logics are combinations of topological and temporal modal logics that are used for reasoning about dynamical systems consisting of a topological space and a continuous function on it. Here we partially solve a major open problem in the field by showing (by reduction of the ω-reachability problem for lossy channel systems) that the dynamic topological logic over arbitrary top...

In this paper, we analyze the main topological properties of a relevant class of topologies associated with spaces ordered by preferences (asymmetric, negatively transitive binary relations). This class consists of certain continuous topologies which include the order topology. The concept of saturated identification is introduced in order to provide a natural proof of the fact that all these s...

Due to importance of the concepts of θ-closure and δ-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy δ-closure by using the concept of quasicoincidence in fuzzy topological spaces. In this paper, we will introduce the concept of δ-closure in intuitionistic fuzzy topological spaces, which is a g...

In this paper, we first generalize a fixed point theorem due to Tarafdar from topological vector spaces to general topological spaces without linear structure. By using our new fixed point theorem, some new existence theorems of solutions for generalized vector equilibrium problems and generalized implicit vector variational inequality problems are proved under noncompact settings of general to...

A.Pushpalatha et al [11] introduced the concept of τ-g-closed set in topological spaces. S.Eswaran and A.Pushpalatha [6] introduced and studied the properties of τ-generalized continuous maps and τ-gc-irresolute maps in topological spaces. In this paper, we introduce and study a new class of maps called τ-generalized open maps and the notion of τ-generalized homeomorphism and τ-gchomeomorphism ...