Dhananjoy Mandal

Bio: Dhananjoy Mandal is an academic researcher from University of Calcutta. The author has contributed to research in topics: Topological space & Ring (mathematics). The author has an hindex of 3, co-authored 17 publications receiving 26 citations.

On a type of generalized closed sets

Abstract: 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.

A class of ideals in intermediate rings of continuous functions

Abstract: For any completely regular Hausdorff topological space X, an intermediate ring A(X) of continuous functions stands for any ring lying between C ∗ (X) and C(X). It is a rather recently established fact that if A(X) ≠ C(X), then there exist non maximal prime ideals in A(X).We offer an alternative proof of it on using the notion of z◦-ideals. It is realized that a P-space X is discrete if and only if C(X) is identical to the ring of real valued measurable functions defined on the σ-algebra β(X) of all Borel sets in X. Interrelation between z-ideals, z◦-ideal and Ʒ A -ideals in A(X) are examined. It is proved that within the family of almost P-spaces X, each Ʒ A -ideal in A(X) is a z◦-ideal if and only if each z-ideal in A(X) is a z◦-ideal if and only if A(X) = C(X).

Proximity structure on generalized topological spaces

Abstract: The aim of the present article is to introduce a kind of proximity structure, termed $$\mu $$ -proximity, on a set X, which ultimately gives rise to a generalized topology on the ambient set X. An alternative description of $$\mu $$ -proximity is given and it is shown that any generalized topology of a generalized topological space $$(X, \mu )$$ is always induced by a suitable $$\mu $$ -proximity if and only if $$(X, \mu )$$ satisfies a type of complete regularity condition. The notion of quasi $$\mu $$ -proximity is also introduced and the desired result that every generalized topology can be achieved from a quasi $$\mu $$ -proximity, is proved.

Soft prime and semiprime int-ideals of a ring

Abstract: In this paper, some properties of soft radical of a soft int-ideal have been developed and soft prime int-ideal, soft semiprime int-ideal of a ring are defined. Several characterizations of soft prime (soft semiprime) int-ideals are investigated. Also it is shown that the direct and inverse images of soft prime (soft semiprime) int-ideals under homomorphism remains invariant.

On some new characterizations of near paracompactness and associated results

Abstract: 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.

On a Simultaneous Generalization of β-Normality and Almost Normality

Abstract: A new generalization of normality called almost $\beta$-normality is introduced and studied which is a simultaneous generalization of almost normality and $\beta$-normality. A topological space is called almost $\beta$-normal if for every pair of disjoint closed sets $A$ and $B$ one of which is regularly closed (Say $A$), there exist disjoint open sets $U$ and $V$ such that $\overline{U \cap V }= A $ , $\overline{U \cap V}= B$ and $\overline{U} \cap \overline{V} = \phi$.

Decompositions of τҁ-Continuity and Continuity

Abstract: Abstract In this paper, we introduce and investigate the notion of weakly ҁ-locally closed sets in a topological space with a grill. Furthermore, by using these sets, we obtain new decompositions of continuity.

On topological structures of virtual fuzzy parametrized fuzzy soft sets

Abstract: With the generalization of the concept of set, more comprehensive structures could be constructed in topological spaces. In this way, it is easier to express many relationships on existing mathematical models in a more comprehensive way. In this paper, the topological structure of virtual fuzzy parametrized fuzzy soft sets is analyzed by considering the virtual fuzzy parametrized fuzzy soft set theory, which is a hybrid set model that offers very practical approaches in expressing the membership degrees of decision makers, which has been introduced to the literature in recent years. Thus, it is aimed to contribute to the development of virtual fuzzy parametrized fuzzy soft set theory. To construct a topological structure on virtual fuzzy parametrized fuzzy soft sets, the concepts of point, quasi-coincident and mapping are first defined for this set theory and some of its characteristic properties are investigated. Then, virtual fuzzy parametrized fuzzy soft topological spaces are defined and concepts such as open, closed, closure, Q-neighborhood, interior, base, continuous, cover and compact are given. In addition, some related properties of these concepts are analyzed. Finally, many examples are given to make the paper easier to understand.

Rings and subrings of continuous functions with countable range

Abstract: Intermediate rings of the functionally countable subalgebra of C(X) (i.e., the rings Ac(X) lying between Cc∗(X) and Cc(X)), where X is a Hausdorff zero-dimensional space, are studied in this article...