Topology Between Two Sets

  • S. Nithyanantha Jothi Department of Mathematics, Aditanar College, Tiruchendur – 628216, India
  • P. Thangavelu Department of Mathematics, Karunya University, Coimbatore - 641 114, India
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 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.

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Published
2017-06-10
Section
Articles