Topology Between Two Sets

Abstract

The aim of this paper is to introduce a single structure which carries the subsets of X as well as the subsets of Y for studying the information about the ordered pair (A, B) of subsets of X and Y. Such a structure is called a binary structure from X to Y. Mathematically a binary structure from X to Y is defined as a set of ordered pairs (A, B) where AX and BY. The purpose of this paper is to introduce a new topology between two sets called a binary topology and investigate its basic properties where a binary topology from X to Y is a binary structure satisfying certain axioms that are analogous to the axioms of topology.

On Binary Generalized Topological Spaces

“…Mathematically a binary structure from X to Y is defined as a set of ordered pairs (A, B) where A ⊆ X and B ⊆ Y . The concept of binary topology from X to Y was introduced by S. Jothi et al [13]. Definition 1.1.…”

“…In 2011, S. Jothi et al [13] introduced a single structure which carries the subsets of X as well as the subsets of Y for studying the information about the ordered pair (A, B) of subsets of X and Y . Such a structure is called a binary structure from X to Y .…”

“…Definition 1.1. [13] If f : Z −→ X × Y is a function and A ⊆ X, B ⊆ Y . We define f −1 (A, B) = {z ∈ Z : f (z) = (x, y) ∈ (A, B)}.…”

Irresoluteness via binary supra topological spaces

“…Govindappa Navalagi 2 studied the class of completely  irresolute function. A function f : X  Y is said to be strongly continuous (strongly  9 . In this paper we introduce binary supra -irresolute functions and also we study about completely -irresolute and strongly -irresolute functions in binary supra topological space.…”