J-Closed Functions via J-Closed Sets in Topological Spaces

Abstract

In this article, J-closed functions using the concept of J-closed sets and J-open functions using the notion of J-open sets are initiated. The interrelationships of these newly introduced functions with various existing functions are examined and its properties are analysed.The composition of two J-closed function need not be a J-closed function which is proved by Counter Example.The J-closed functions are used to define homeomorphisms using J-closed sets in topological spaces.Homeomorphisms are the isomorphisms in the category of topological spaces-that is, they are the mappings that preserve all the topological properties of a given space.

The study of J-closed functions has been done by the following methods:

• Analytical method of comparing J-closed functions with other existing closed functions.
• Obtaining counter examples wherever necessary to substantiate the result.
• Interpreting the results as diagrams.
• Analysis of preservation of topological properties by J-closed functions.