# Topology Between Two Sets

Keywords:
Binary topology, binary open, binary closed, binary closure, binary interior, and binary continuity.

### 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 AX and BY. 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.