A Study on Continuity functions in Neutro-Topological Spaces

Bhimraj Basumatary; Jeevan Krishna Khaklary

Authors

Bhimraj Basumatary Department of Mathematics, Central Institute of Technology, Kokrajhar, Assam, India;
Jeevan Krishna Khaklary Department of Mathematical Sciences, Bodoland University, Assam, India;

Keywords:

Neutro-topological space, neutro-continuity, weakly neutro-continuity, neutro-open map, neutro-closed map, neutro-homeomorphism

Abstract

The specific purpose of this study is to define continuity of mappings in
neutro-topological spaces using neutro-open and neutro-closed sets and analyze the properties of
continuous functions that are true in classical topological spaces in the neutro-topological space.
Neutro-interior and neutro-closure in neutro-topological spaces have some properties that are
somewhat different from those in classical topological spaces. However, with the definition of a
new form of continuity, termed as weakly neutro-continuity, much of the properties of continuous
functions could be established in neutro-topological spaces. Neutro-open map and neutro-closed
maps are also defined on the basis of neutro-open and neutro-closed sets. The notion of weakly
neutro-continuity has been used to define neutro-homeomorphism and many of the properties of
homeomorphism are analyzed and found to be true in the case of neutro-homeomorphism. A
comparison of some of the properties of continuity and homeomorphism in classical topological
spaces have been done vis-à-vis the neutrosophic topological spaces and neutro-topological spaces.

DOI: 10.5281/zenodo.14295798