In this paper we introduce the concept of -closed sets and investigate some of its properties in the spaces considered by A. D. Alexandroff [1] where only countable unions of open sets are required to be open. We also introduce a new separation axiom called -axiom in the Alexandroff spaces with the help of -closed sets and investigate some of its consequences.
Given a space , its -subsets form a basis of a new space , called the -modification of . We study how the assumption that the -modification is homogeneous influences properties of . If is first countable, then is discrete and, hence, homogeneous. Thus, is much more often homogeneous than itself. We prove that if is a compact Hausdorff space of countable tightness such that the -modification of is homogeneous, then the weight of does not exceed (Theorem 1). We also establish...
-separation axioms are introduced in ordered fuzzy topological spaces and some of their basic properties are investigated besides establishing an analogue of Urysohn’s lemma.
An overview of generated triangular norms and their applications is presented. Several properties of generated -norms are investigated by means of the corresponding generators, including convergence properties. Some applications are given. An exhaustive list of relevant references is included.
In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.
For a locally symmetric space , we define a compactification which we call the “geodesic compactification”. It is constructed by adding limit points in to certain geodesics in . The geodesic compactification arises in other contexts. Two general constructions of Gromov for an ideal boundary of a Riemannian manifold give for locally symmetric spaces. Moreover, has a natural group theoretic construction using the Tits building. The geodesic compactification plays two fundamental roles in...