Meekly SC∗-Normal Spaces in Topological Spaces | Chapter 8 | Mathematics and Computer Science: Research Updates Vol. 9

 

This chapter develops the concept of meekly SC∗-normality, a novel generalization of the classical notion of normality in topology. The proposed framework simultaneously broadens SC∗-normality and other established forms of normality, offering a unified perspective on generalized separation axioms. Fundamental properties are systematically derived, several equivalent characterizations are obtained, and the relationships between meekly SC∗-normal spaces and a range of existing normal-type spaces are rigorously analyzed. By establishing these structural connections, the chapter not only enriches the theory of generalized closed sets and separation axioms but also opens new directions for further research in advanced topological studies.

 

Author(s) Details

Neeraj K. Toma
Department of Applied Mathematics, Gautam Buddha University, Greater Noida, India .

 

Saroj Rani
Department of Mathematics, S. A. Jain (PG) College, Ambala City, Haryana, India.

 

Please see the book here :- https://doi.org/10.9734/bpi/mcsru/v9/6714

A Discussion on Some Topological and Algebraic Features of Symmetric Spaces | Chapter 3 | Mathematics and Computer Science: Contemporary Developments Vol. 10

Many scientific problems in various fields may have their own conditions that might not agree with the geometric structure and properties of some spaces familiar to mathematicians and geometers. Many properties of symmetric spaces can be studied through their Lie algebras and root systems, and especially the problem of classification of symmetric spaces.

This study introduced some approaches, geometrical and algebraic, which help to give a further understanding of symmetric spaces. Symmetric space is a very important field for understanding abstract and applied features of spaces. This study also introduced Riemannian Manifold, Lie groups and Lie algebras, and some of their topological and algebraic properties, with some concentration on Lie algebras and root systems, which help classification and many applications of symmetric spaces. The paper is an attempt to explain some algebraic features of symmetric spaces and how to get some of their properties using an algebraic approach, concluded with some results.

 

Author (s) Details

 

Umsalama Ahmed Abd Alla Elemam
Department of Mathematics, Jazan University Al- Dayer University College, Kingdom of Saudi Arabia.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v10/3301

δJ-Closed Sets in Topological Spaces | Chapter 7 | Novel Research Aspects in Mathematical and Computer Science Vol. 6

 

δJ-closed sets, a brand-new type of sets, are introduced in topological spaces in this chapter. Analyses are done on the characteristics and connections to other g-closed sets. We acquire some significant characterizations.

Author(s) Details:

K. P. Vethavarna,
Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women Coimbatore, India.

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

Please see the link here: https://stm.bookpi.org/NRAMCS-V6/article/view/7766