Papers by Dhananjoy Mandal
arXiv (Cornell University), Apr 15, 2023
Let P be an ideal of closed subsets of a topological space X. Consider the ring, C(X) P of real v... more Let P be an ideal of closed subsets of a topological space X. Consider the ring, C(X) P of real valued functions on X whose closure of discontinuity set is a member of P. We investigate the ring properties of C(X) P for different choices of P, such as the ℵ 0 -self injectivity and regularity of the ring, if and when the ring is Artinian and/or Noetherian. The concept of F P -space was introduced by Z. Gharabaghi, M. Ghirati and A. Taherifar in 2018 in a paper published in Houston Journal of Mathematics. In this paper, they established a result stating that every P -space is a F P -space. We furnish that this theorem might fail if X is not Tychonoff and we provide a suitable counter example to prove our assertion.
Boletim da Sociedade Paranaense de Matemática, 2012
The purpose of this paper is to introduce and study a new class of generalized closed sets in a t... more The purpose of this paper is to introduce and study a new class of generalized closed sets in a topological space X, defined in terms of a grill G on X. Explicit characterization of such sets along with certain other properties of them are obtained. As applications, some characterizations of regular and normal spaces are achieved by use of the introduced class of sets.
Positivity, 2022
There are three famous results in the field of rings of real valued continuous functions namely, ... more There are three famous results in the field of rings of real valued continuous functions namely, M. H. Stone Theorem, Urysohn’s Extension Theorem and Gelfand Kolmogoroff Theorem. We study analogous results for rings of functions satisfying the property mentioned in the tittle of this article.
Armenian Journal of Mathematics
In this paper, the notion of the soft Jacobson radical of a ring is defined. A relationship betwe... more In this paper, the notion of the soft Jacobson radical of a ring is defined. A relationship between the soft Jacobson radical of a ring and Jacobson semisimple ring is established. Some properties of this notion have been studied under homomorphism.
Matematički Vesnik, 2014
The idea of countable near paracompactness of a topological space, as a natural oshoot of the wel... more The idea of countable near paracompactness of a topological space, as a natural oshoot of the well known concept of near paracompactness, is introduced and investigated in this article. In the process, the notion of semi nearly normal spaces is initiated. Apart from its char- acterizations, semi near normality is used for the investigation of countably nearly paracompact spaces.
In this paper we investigate N(k)-paracontact metric manifolds satisfying the curvature condition... more In this paper we investigate N(k)-paracontact metric manifolds satisfying the curvature conditions R · Z = 0 and Z ·S = 0, where R, Z and S are the Riemannian curvature tensor, the concircular curvature tensor and Ricci tensor, respectively. Further, we study N(k)-paracontact metric manifolds satisfying the curvature conditions Z·Z = 0 and Z ·R = 0.
The purpose of this paper is to study conformally flat (Error rendering LaTeX formula) -paraconta... more The purpose of this paper is to study conformally flat (Error rendering LaTeX formula) -paracontact metric manifolds. Also we study (Error rendering LaTeX formula) -Ricci solitons on three-dimensional (Error rendering LaTeX formula) -paracontact metric manifolds. Finally, we study gradient Ricci solitons on three-dimensional contractible (Error rendering LaTeX formula) -paracontact metric manifolds.
In this paper we introduce certain new types of sets in a generalized topological space via hered... more In this paper we introduce certain new types of sets in a generalized topological space via hereditary classes and investigate their several properties. In the process we achieve some nice applications of these newly defined sets to study a few lower separation properties viz μ-R0, μ -R1 and μ ∗-T 1 2 spaces. 2000 Mathematics Subject Classification: 54A05, 54A10, 54D10.
Near paracompactness is a concept, in Set Topology, which is weaker than paracompactness; in this... more Near paracompactness is a concept, in Set Topology, which is weaker than paracompactness; in this paper, several characterizations of this concept have been enunciated and proved. In the process, several tools have been utilized. The main theorem uses the selection theory of Michael.
A proper ideal $I$ in a commutative ring with unity is called a $z^\circ$-ideal if for each $a$ i... more A proper ideal $I$ in a commutative ring with unity is called a $z^\circ$-ideal if for each $a$ in $I$, the intersection of all minimal prime ideals in $R$ which contain $a$ is contained in $I$. For any totally ordered field $F$ and a completely $F$-regular topological space $X$, let $C(X,F)$ be the ring of all $F$-valued continuous functions on $X$ and $B(X,F)$ the aggregate of all those functions which are bounded over $X$. An explicit formula for all the $z^\circ$-ideals in $A(X,F)$ in terms of ideals of closed sets in $X$ is given. It turns out that an intermediate ring $A(X,F)\neq C(X,F)$ is never regular in the sense of Von-Neumann. This property further characterizes $C(X,F)$ amongst the intermediate rings within the class of $P_F$-spaces $X$. It is also realized that $X$ is an almost $P_F$-space if and only if each maximal ideal in $C(X,F)$ is $z^\circ$-ideal. Incidentally this property also characterizes $C(X,F)$ amongst the intermediate rings within the family of almost $P...
... On a generalization of S-closedness for topological spaces via ideals. Autores: Dhananjoy Man... more ... On a generalization of S-closedness for topological spaces via ideals. Autores: Dhananjoy Mandal; Localización: Revista de la Academia Canaria de Ciencias: = Folia Canariensis Academiae Scientiarum, ISSN 1130-4723, Vol. 21, Nº. 1-2, 2009 , págs. 95-106. ...
New Mathematics and Natural Computation
The relation between soft element-wise field and soft int-field has been established and then som... more The relation between soft element-wise field and soft int-field has been established and then some properties of soft int-field are studied. We define the notions of soft algebraic element and soft purely inseparable element of a soft int-field extension. Some characterizations of soft algebraic and soft purely inseparable int-field extensions are given. Lastly, we define soft separable algebraic int-field extension and study some of its properties.
New Mathematics and Natural Computation
In this paper, the notion of soft elementwise ring is introduced and it is shown that the concept... more In this paper, the notion of soft elementwise ring is introduced and it is shown that the concepts of soft elementwise ring and soft int-ring of a ring are equivalent. The concept of soft direct sum of soft int-rings is defined and some equivalent conditions are given. The notions of minimal generating set for a soft int-ideal and soft principal int-ideal are presented. Some properties of soft principal int-ideal are discussed.
Afrika Matematika
The aim of the present article is to introduce a kind of proximity structure, termed $$\mu $$μ-pr... more The aim of the present article is to introduce a kind of proximity structure, termed $$\mu $$μ-proximity, on a set X, which ultimately gives rise to a generalized topology on the ambient set X. An alternative description of $$\mu $$μ-proximity is given and it is shown that any generalized topology of a generalized topological space $$(X, \mu )$$(X,μ) is always induced by a suitable $$\mu $$μ-proximity if and only if $$(X, \mu )$$(X,μ) satisfies a type of complete regularity condition. The notion of quasi $$\mu $$μ-proximity is also introduced and the desired result that every generalized topology can be achieved from a quasi $$\mu $$μ-proximity, is proved.
In this paper, we study some properties of the ring C(X)F of all real valued functions which are ... more In this paper, we study some properties of the ring C(X)F of all real valued functions which are continuous except on some finite subsets of X. We show that C(X)F is closed under uniform limit if and only if the set of all non-isolated points of X is finite. We also initiate and investigate the zero divisor graph of the ring C(X)F .
New Mathematics and Natural Computation
The main aim of this paper is to establish the concepts of soft seminorm and soft norm with the h... more The main aim of this paper is to establish the concepts of soft seminorm and soft norm with the help of balanced, absorbing and convex soft sets. Also, we have established equivalent concepts of soft seminorm as well as of soft norm.
SERIES III - MATEMATICS, INFORMATICS, PHYSICS
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Papers by Dhananjoy Mandal