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

J-closed functions using the idea of J-closed sets and J-open functions using the concept of J-open sets are introduced in this article. The features of these newly added functions are studied, as well as their interrelationships with other functions. Counter Example proves that the combination of two J-closed functions does not have to be a J-closed function. In topological spaces, J-closed functions are used to define homeomorphisms using J-closed sets. Homeomorphisms are isomorphisms in the category of topological spaces, that is, mappings that preserve all of a particular space’s topological attributes. The following approaches have been used to investigate J-closed functions:

Analytical approach for comparing J-closed functions to other closed functions that already exist.

Whenever possible, obtaining counter instances to corroborate the findings.

Using diagrams to interpret the results.

J-closed functions are used to study the preservation of topological characteristics.

**Author(s) Details:**

**P. L. Meenakshi,
**Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, India.

**R. Sudha,
**Department of Mathematics, Dr. N.G.P. Institute of Technology, Coimbatore, India.

**Please see the link here:** **https://stm.bookpi.org/NRAMCS-V4/article/view/7037**