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.
 MSC 2010: 54A05, 54A99.

F-Bipolar metric spaces and fixed point theorems with applications

“…The definitions of completeness, convergence, and Cauchy sequence in this setting can be found in [7]. In 2011, Jothi et al [8] introduced the notion of binary topology to define a topology between two sets.…”

WEAKLY BINARY gα – CLOSED SETS AND WEAKLY BINARY αg – CLOSED SETS IN BINARY TOPOLOGICAL SPACE

“…Maki et.al [4,5] introduced and studied generalized α-closed sets and α-generalized closed sets. In 2011, S.Nithyanantha Jothi and P.Thangavelu [6] introduced topology between two sets and also studied some of their properties. Topology between two sets is the binary structure from X to Y which is defined to be the ordered pairs (A, B) where A ⊆ X and B ⊆ Y.…”

“…Let X and Y be any two nonempty sets. A binary topology [6] from X to Y is a binary structure ℳ ⊆ ℙ(X) × ℙ(Y) that satisfies the axioms namely 1. (ϕ, ϕ) and (X, Y) ∈ ℳ, 2.…”

Exploring Quantum and Binary Soft í µí»¼–Open Sets:Practical Applications through Soft Topologies

“…A mathematical structure that carries the collection of subsets of two universal sets is known as binary topology. Binary topology was presented by Nithyananda Jothi and Thangavelu [18] as a concept of topology between two universal sets. Ahu Acikgoz and Nihal Tas [1] presented a binary soft set (BSS) based on two initial universes and a group of parameters in 2016 and investigated its essential structures.…”