arXiv subjects

Neeraj Kumar Tomar

Publications and source records attributed to Neeraj Kumar Tomar.

9 recordsLinked to original sources

arXiv2026

Meekly SC*-Normal Spaces in Topological Spaces

This chapter develops the concept of \textbf{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.

math.GN↗

arXiv2025

Idempotent & Nilpotent Operators and Matrices in Bicomplex Space

This paper explores idempotent and nilpotent operators in bicomplex spaces, focusing on their properties and behavior. We define idempotent and nilpotent matrices in this framework and derive related results. Several theorems are presented to establish conditions for the existence and behavior of bicomplex idempotent and nilpotent operators and bicomplex idempotent matrices.

math.RT↗

arXiv2025

H*-Normal Spaces and Some Related Functions

This paper introduces and explores functions defined on $ H^* $-normal spaces through the framework of $ H^* $-open sets. We extend the concept of $ H^* $-normality and investigate its connections with $ g $-normal and classical normal spaces. Additionally, we generalize $ H^* $-closed and $ H^* $-generalized closed functions, analyzing their fundamental properties. Several characterizations of $ H^* $-normal spaces are established, along with preservation theorems that highlight the structural significance of these functions.

math.GN↗

arXiv2025

Some Separation Axioms in Topological Spaces

In this paper, we introduced the concepts of new separation axioms called $ SC^* $-separation axioms and $ H^* $-separation axioms by using $ SC^* $ and $ H^* $-open sets in topological spaces. The $ SC^* $-separation axioms include $ SC^* $-$ C_0 $, $ SC^* $-$ C_1 $, weakly $ SC^* $-$ C_0 $, and weakly $ SC^* $-$ C_1 $ spaces, while the $ H^* $-separation axioms include $ H^* $-$ T_{\frac{1}{2}} $, $ H^* $-$ T_b $, and $ H^* $-$ T_d $ spaces. Also, we obtained several properties of such spaces.

math.GN↗

arXiv2025

Q*-normal spaces

In this paper, using Q*-closed sets, we introduce a new version of normality called, Q*-normality which is a weak form of normality. Further utilizing Q*g-closed sets, we obtain some characterizations of Q*-normal and normal spaces and also obtain some preservation theorems for Q*-normal spaces.

math.GN↗

arXiv2025

Almost SC*-normal spaces

This paper introduces and investigates a new class of almost normal spaces, referred to as almost SC*-normal spaces, which are defined using SC*-open sets. Building on the work of A. Chandrakala and K. Bala Deepa Arasi, we explore several properties of these spaces within the framework of topology. Moreover, we obtain some new characterizations and preservation theorems of almost SC*-normal spaces.

math.GN↗

arXiv2025

Softly $πg\hat{D}$-Normal Spaces

The aim of this paper is to introduce a new class of softly normal called softly $πg\widehat{D}$ -normality by using $πg\widehat{D}$ -open sets and obtained several properties of such a space. We discuss many properties of this new space and we give some properties that connect this new spaces with some other topological spaces, also we present some examples and counter examples that show the relationships between softly $πg\widehat{D}$ -normal spaces and some other topological spaces, also we introduced the concept of $πg\widehat{D}$ -normal, almost $πg\widehat{D}$ -normal, quasi $πg\widehat{D}$ -normal, mildly $πg\widehat{D}$ -normal. The main result of this paper is that softly $πg\widehat{D}$ -normality is a topological property and it is a hereditary property with respect to closed domain subspaces. Moreover, we obtain some new characterizations and preservation theorems of softly $πg\widehat{D}$ -normal spaces. We insure that existence of utility for new results of softly $πg\widehat{D}$ -normality using separation axioms in topological spaces which is separate on a known separation axioms in topological spaces.

math.GN↗

arXiv2025

SC*-Regular spaces and some functions

This paper introduces a novel class of topological spaces, termed SC*-regular spaces, which are defined using SC*-open sets. We explore their fundamental properties and examine their connections with existing regularity concepts, such as regular, almost, softly, weakly, alpha, zeta, and generalized-regular spaces respectively. Furthermore, we examined and define, analyze generalized SC*-closed sets and SC*-generalized closed functions, establishing key properties and preservation theorems. Several characterizations of SC*-regular spaces are also presented, providing new insights into generalized regularity in topology.

math.GN↗

arXiv2025

SC*-Normal spaces and some functions

In this paper, we introduce and explore a new class of topological spaces termed as SC*-normal spaces, defined via SC*-open sets. The concept of SC*-normality is analyzed in relation to classical notions such as normal spaces and g-normal spaces. We further define and examine generalized forms of SC*-closed functions, including SC*-generalized closed mappings, and investigate their fundamental properties. Several characterizations of SC*-normal spaces are established, and various preservation theorems under different types of functions are also presented.

math.GN↗