S. Acharyya

activity

20172026

most citedOrdered field valued continuous functions with countable range

4 citations · 7 across the 19 of their papers we have counts for

collaborators

23 papers

math.GN2026

A topological view of algebraic structures in $C_{p} (X)$

Pratip Nandi, Soumajit Dey, Amrita Dey +1

This manuscript focuses on the topological behaviour of algebraic structures in $C_{p} (X)$ . Closure of ideals in $C_{p} (X)$ is determined and are used to characterise various topologic…

math.GN2026

A special kind of topology on $C (X)$ lying between the point-open topology and the topology of uniform convergence

Soumajit Dey, Sudip Kumar Acharyya, and Dhananjoy Mandal

Let $X$ be a topological space. For each transfinite cardinal number $ℵ_{α}$ , we define a topology $C_{ℵ_{α}} (X)$ on the ring $C (X)$ . With $ℵ_{α} = ℵ_{0}$ , $C_{\aleph_α}(…

math.GN2025

Measure finite topology on the ring of measurable functions

Soumajit Dey, Sudip Kumar Acharyya, Dhananjoy Mandal

Let $M (X, A, μ)$ be the ring of all real-valued measurable functions constructed over a measure space $(X, A, μ)$ . A topology on $\mathcal{M}(X,\mathcal{A…

math.GN2025

A number of properties enjoyed by two specially constructed topologies on $C (X)$

Soumajit Dey, Sudip Kumar Acharyya, Dhananjoy Mandal

If $I$ is an ideal in the ring $C (X)$ of all real valued continuous functions defined over a Tychonoff space $X$ , then $X$ is called $I$ - $p se u d oco m p a c t$ if the set $X\setminus \big…

math.GN2024

Structure spaces and allied problems on a class of rings of measurable functions

Soumajit Dey, Sudip Kumar Acharyya, Dhananjoy Mandal

A ring $S (X, A)$ of real valued $A$ -measurable functions defined over a measurable space $(X, A)$ is called a $χ$ -ring if for each $E \in A$ ,…

math.GM2023

Some familiar graphs on the rings of measurable functions

Pratip Nandi, Atasi Deb Ray, Sudip Kumar Acharyya

In this paper, replacing `equality' by 'equality almost everywhere' we modify several terms associated with the ring of measurable functions defined on a measure space $(X, \mathca…

math.GN2023

More on generalizations of topology of uniform convergence and $m$ -topology on $C (X)$

Pratip Nandi, Rakesh Bharati, Atasi Deb Ray +1

This paper conglomerates our findings on the space $C (X)$ of all real valued continuous functions, under different generalizations of the topology of uniform convergence and the $m…

math.GN2023

$U$ -topology and $m$ -topology on the ring of Measurable Functions, generalized and revisited

Pratip Nandi, Atasi Deb Ray, Sudip Kumar Acharyya

Let $M (X, A)$ be the ring of all real valued measurable functions defined over the measurable space $(X, A)$ . Given an ideal $I$ in $\mathcal{M}(X,\math…

math.GN2023

Rings of functions whose closure of discontinuity set is in an ideal of closed sets

Amrita Dey, Sudip Kumar Acharyya, Sagarmoy Bag +1

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…

math.FA2022

A Generalization of $m$ -topology and $U$ -topology on rings of measurable functions

Soumyadip Acharyya, Rakesh Bharati, Atasi Deb Ray +1

For a measurable space ( $X, A$ ), let $M (X, A)$ be the corresponding ring of all real valued measurable functions and let $μ$ be a measure on ($X,\mathca…

math.GN2022

Zero-divisor graph and comaximal graph of rings of continuous functions with countable range

Rakesh Bharati, Amrita Acharyya, A. Deb Ray +1

In this paper, two outwardly different graphs, namely, the zero divisor graph $Γ (C_{c} (X))$ and the comaximal graph $Γ_{2}^{^{'}} (C_{c} (X))$ of the ring $C_{c} (X)$ of all real-valued continuo…

math.GM2022

Annihilator graph of the ring $C_{P} (X)$

Pratip Nandi, Sudip Kumar Acharyya, Atasi Deb Ray

In this article, we introduce the annihilator graph of the ring $C_{P} (X)$ , denoted by $A G (C_{P} (X))$ and observe the effect of the underlying Tychonoff space $X$ o…

math.AC2021★ 2 cited

Zero-divisor graph of the rings $C_{P} (X)$ and $C_{\infty}^{P} (X)$

Sudip Kumar Acharyya, Atasi Deb Ray, Pratip Nandi

In this article we introduce the zero-divisor graphs $Γ_{P} (X)$ and $Γ_{\infty}^{P} (X)$ of the two rings $C_{P} (X)$ and $C_{\infty}^{P} (X)$ ; here $\math…

math.GN2020★ 1 cited

Intrinsic characterizations of $C$ -realcompact spaces

Sudip Kumar Acharyya, Rakesh Bharati, Atasi Deb Ray

$c$ -realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41(8), 2018, 1135-1167. We offer a characterization of these spaces $X$ via $c$ -stable family of c…

math.GN2020★ 4 cited

Ordered field valued continuous functions with countable range

Sudip Kumar Acharyya, Atasi Deb Ray, Pratip Nandi

For a Hausdorff zero-dimensional topological space $X$ and a totally ordered field $F$ with interval topology, let $C_{c} (X, F)$ be the ring of all $F -$ valued continuous functions on…

math.GN2020

On Cardinality Of Non Isomorphic Intermediate Rings Of C(X)

Bedanta Bose

Let $\sum (X)$ be the collection of subalgebras of $C (X)$ containing $C^{*} (X)$ , where $X$ is a Tychonoff space. For any $A (X) \in \sum (X)$ there is associated a subset $\upsilon_{A…

math.GN2020

Intermediate rings of complex-valued continuous functions

Amrita Acharyya, Sudip Kumar Acharyya, Sagarmoy Bag +1

Let $Σ (X, C)$ denote the collection of all the rings between $C^{*} (X, C)$ and $C (X, C)$ . We show that there is a natural correlation between the absolutely c…

math.GN2019

Rings and subrings of continuous functions with countable range

Sudip Kumar Acharyya, Rakesh Bharati, A. Deb Ray

Intermediate rings of real valued continuous functions with countable range on a Hausdorff zero-dimensional space $X$ are introduced in this article. Let $Σ_{c} (X)$ be the family of…

math.GN2018

Recent progress in Rings and Subrings of Real Valued Measurable Functions

Soumyadip Acharyya, Sudip Kumar Acharyya, Sagarmoy Bag +1

Two separated realcompact measurable spaces $(X, A)$ and $(Y, B)$ are shown to be isomorphic if and only if the rings $M (X, A)$ and $\mathcal{M…

math.FA2018

Ideals in Rings and Intermediate Rings of Measurable Functions

Sudip Kumar Acharyya, Sagarmoy Bag, Joshua Sack

The set of all maximal ideals of the ring $M (X, A)$ of real valued measurable functions on a measurable space $(X, A)$ equipped with the hull-kernel top…

math.GN2018

Abundance of Isomorphic and non isomorphic intermediate rings

Bedanta Bose, Sudip Kumar Acharyya

It is well known that for a non pseudocompact space X, the family (X) of all intermediate subrings of C(X) which contain bounded real valued continuous functions contains at least…

math.GN2017

Some new results on functions in $C (X)$ having their support on ideals of closed sets

Sagarmoy Bag, Sudip Kumar Acharyya, Pritam Rooj +1

For any ideal $P$ of closed sets in $X$ , let $C_{P} (X)$ be the family of those functions in $C (X)$ whose support lie on $P$ . Further let $C^\mathcal{P}_…

math.GN2017

$z^{\circ}$ -ideals in intermediate rings of ordered field valued continuous functions

Sagarmoy Bag, Sudip Kumar Acharyya, Dhananjoy Mandal

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 con…

A topological view of algebraic structures in Cp​(X)

A special kind of topology on C(X) lying between the point-open topology and the topology of uniform convergence

Measure finite topology on the ring of measurable functions

A number of properties enjoyed by two specially constructed topologies on C(X)

Structure spaces and allied problems on a class of rings of measurable functions

Some familiar graphs on the rings of measurable functions

More on generalizations of topology of uniform convergence and m-topology on C(X)

U-topology and m-topology on the ring of Measurable Functions, generalized and revisited

Rings of functions whose closure of discontinuity set is in an ideal of closed sets

A Generalization of m-topology and U-topology on rings of measurable functions

Zero-divisor graph and comaximal graph of rings of continuous functions with countable range

Annihilator graph of the ring CP​(X)

Zero-divisor graph of the rings CP​(X) and C∞P​(X)

Intrinsic characterizations of C-realcompact spaces

Ordered field valued continuous functions with countable range

On Cardinality Of Non Isomorphic Intermediate Rings Of C(X)

Intermediate rings of complex-valued continuous functions

Rings and subrings of continuous functions with countable range

Recent progress in Rings and Subrings of Real Valued Measurable Functions

Ideals in Rings and Intermediate Rings of Measurable Functions

Abundance of Isomorphic and non isomorphic intermediate rings

Some new results on functions in C(X) having their support on ideals of closed sets

z∘-ideals in intermediate rings of ordered field valued continuous functions

A topological view of algebraic structures in $C_{p} (X)$

A special kind of topology on $C (X)$ lying between the point-open topology and the topology of uniform convergence

A number of properties enjoyed by two specially constructed topologies on $C (X)$

More on generalizations of topology of uniform convergence and $m$ -topology on $C (X)$

$U$ -topology and $m$ -topology on the ring of Measurable Functions, generalized and revisited

A Generalization of $m$ -topology and $U$ -topology on rings of measurable functions

Annihilator graph of the ring $C_{P} (X)$

Zero-divisor graph of the rings $C_{P} (X)$ and $C_{\infty}^{P} (X)$

Intrinsic characterizations of $C$ -realcompact spaces

Some new results on functions in $C (X)$ having their support on ideals of closed sets

$z^{\circ}$ -ideals in intermediate rings of ordered field valued continuous functions