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Argha Ghosh

Publications and source records attributed to Argha Ghosh.

11 recordsLinked to original sources
arXiv2025

More about cofinally Bourbaki quasi-complete metric spaces

We characterize cofinally Bourbaki quasi-complete metric spaces and their completions in terms of certain Lipschitz-type functions. To this end, we introduce and study a new class of functions, namely strongly uniformly locally Lipschitz functions, which lie strictly between Lipschitz functions and uniformly locally Lipschitz functions. We show that a metric space is cofinally Bourbaki quasi-complete if and only if the class of strongly uniformly locally Lipschitz functions on coincides with the (a priori) larger class of locally Lipschitz functions. Moreover, the completion of is cofinally Bourbaki quasi-complete if and only if the class of strongly uniformly locally Lipschitz functions agrees with the class of Cauchy-Lipschitz functions. Finally, we provide several characterizations of cofinally Bourbaki quasi-complete metric spaces and their completions using functions that preserve certain classes of Cauchy-type sequences.

math.GN↗
arXiv2025

Uniformly Star Superparacompact Subsets and Spaces

Uniformly star superparacompactness, which is a topological property between compactness and completeness, can be characterized using finite-component covers and a measure of strong local compactness. Using these finite-component covers and the associated functional, we introduce and investigate a variational notion of uniformly star superparacompact subsets in metric spaces in the spirit of studies on uniformly paracompact subset and UC-subset. We show that the collection of all such subsets forms a bornology with a closed base, which is contained in the bornology of uniformly paracompact subsets. Conditions under which these two bornologies coincide are specified. Furthermore, we provide several new characterizations of uniformly star superparacompact metric spaces also known as cofinally Bourbaki-quasi complete spaces in terms of some geometric functionals. As a consequence, we establish new relationships among metric spaces that lie between compactness and completeness.

math.GN↗
arXiv2024

On Multi-Split Continuity and Split Homeomorphisms

We introduce multi-split continuous functions between topological spaces, a weaker form of continuity that generalizes split continuity while being stable under compositions. We will define the associated star multifunction and pre-multi-split multifunctions. Moreover, we will prove that multi-split continuity naturally emerges as the continuity property of selections of finite usco maps, relating their study to set-valued analysis. Finally, we introduce split homeomorphisms and split homeomorphic spaces, showing that for compact, regular Hausdorff spaces, split homeomorphisms characterize deformations with cuts and subsequent re-glues.

math.GN↗
arXiv2018

Rough I-statistical convergence of sequences

The concept of I-statistical convergence of sequence was first defined by Das et.al [2]. In this paper we introduce and study the notion of rough I-statistical convergence of sequence in normed linear Spaces. We also define the set of rough I-statistical limits of a sequence and discuss some topological properties of this set.

math.FA↗
arXiv2018

Generalized Statistical limit points and cluster points via ideal

In this paper we have extended the notion of statistical limit point as introduced by Fridy[8] to I-statistical limit point of sequences of real numbers and studied some basic properties of the set of all I-statistical limit points and I-statistical cluster points of real sequences.

math.FA↗
arXiv2017

Rough I-statistical convergence of double sequence

The concept of I-statistical convergence of a double sequence was first introduced and study by Das et. el [2]. Here in this paper we discuss some results on rough ideal statistical convergence and also we introduce the notion of rough ideal limit set and discuss some topological aspects on this set.

math.FA↗
arXiv2017

On I-statistical cluster point of double sequences

In this paper we are concerned with the recent summability notion of I-statistically pre-Cauchy real double sequences in line of Das et. al. [6] as a generalization of I-statistical convergence. Here we introduce the notion of double I-natural density and present some interesting properties of I-statistically pre-Cauchy double sequences of real numbers. Also in this paper we investigate the notion of I-statistical cluster point of double sequences in finite dimensional normed space.

math.FA↗
arXiv2016

New Types of Convergence on Time Scales

This paper is discussing about the notion of some new types of convergences namely $I$-convergence and $I^*$-convergence of a $Δ$-measurable function $f$ on time scales $T$ by considering ideal on time scales $T$. This idea is further extended to the notion of statistical convergence of a $Δ$-measurable function $f$ on time scales $T$.

math.FA↗
arXiv2016

Strong $I$ AND $I^*$-statistically pre-Cauchy double sequences in Probabilistic Metric Spaces

In this paper we consider the notion of strong $I$-statistically pre-Cauchy double sequences in probabilistic metric spaces in line of Das et. al. [6] and introduce the new concept of strong $I^*$-statistically pre-Cauchy double sequences in real line as well as in probabilistic metric spaces. We mainly study inter relationship among strong $I$-statistical convergence, strong $I$-statistical pre-Cauchy condition and strong $I^*$-statistical pre-Cauchy condition for double sequences in probabilistic metric spaces and examine some basic properties of these notions.

math.FA↗