University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

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. © 2021 World Scientific Publishing Company.

World University root node

Pure Mathematics

New Mathematics and Natural Computation

Soft Int-Field Extension

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. © 2020 World Scientific Publishing Company.

Soft Direct Sum of Soft Int-Rings and Soft Principal Int-Ideal

In this paper we investigate generalized (k, µ)-paracontact metric manifolds satisfying the curvature conditions R · P = 0 and P · S = 0, where R, P and S are the Riemannian curvature tensor, the projective curvature tensor and the Ricci tensor, respectively. Next, we study ξ-projectively flat generalized (k, µ)-paracontact metric manifolds. Further, we study generalized (k, µ)-paracontact metric manifolds satisfying the curvature condition P (X, Y) · φ = 0. Finally, we have cited an example of a generalized (k, µ)-paracontact metric manifold. © 2020, Transilvania University of Brasov 1. All rights reserved.

Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics

On a type of generalized (K, µ)-paracontact metric manifolds

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. © 2020 World Scientific Publishing Company.

A Note on Soft Seminorm and Soft Norm

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. © 2020 the Author(s).

Fulltext

AIMS Mathematics

Soft prime and semiprime int-ideals of a ring

In this paper, the concepts of soft maximal int-ideal and soft irreducible int-ideal of a ring are introduced and some properties of these notions have been studied. Also we point out some facts of a ring which cannot be extended to the soft setting and it is justified by suitable examples. © 2020 World Scientific Publishing Company.

Soft Maximal and Irreducible Int-Ideals of a Ring

For any completely regular Hausdorff topological space X, an inter- mediate 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 ZA-ideals in A(X) are examined. It is proved that within the family of almost P-spaces X, each ZA-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). © 2019, Universitat Politecnica de Valencia. All rights reserved.

GENERAL

Applied General Topology

A class of ideals in intermediate rings of continuous functions

The aim of the present article is to introduce a kind of proximity structure, termed μ-proximity, on a set X, which ultimately gives rise to a generalized topology on the ambient set X. An alternative description of μ-proximity is given and it is shown that any generalized topology of a generalized topological space (X, μ) is always induced by a suitable μ-proximity if and only if (X, μ) satisfies a type of complete regularity condition. The notion of quasi μ-proximity is also introduced and the desired result that every generalized topology can be achieved from a quasi μ-proximity, is proved. © 2018, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.

Afrika Matematika

Proximity structure on generalized topological spaces

In the present paper we study contact metric manifolds whose characteristic vector field ξ belonging to the k-nullity distribution. First we consider concircularly pseudosymmetric N(k)-contact metric manifolds of dimension (2n + 1). Beside these, we consider Ricci solitons and gradient Ricci solitons on three dimensional N(k)-contact metric manifolds. As a consequence we obtain several results. Finally, an example is given. © 2018 Tamkang University. All Rights Reserved.

Tamkang Journal of Mathematics

Certain results on N(k)-contact metric manifolds

In this paper we study certain curvature properties of Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we investigate Weyl projective symmetric Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Next, we study Kenmotsu manifolds satisfying the curvature condition P·S = 0, where P and S are the projective curvature tensor and Ricci tensor respectively with respect to the quartersymmetric metric connection. Further, we discuss about pseudoprojectively flat and φ-projectively semisymmetric Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Finally, we give an example of a 5-dimensional Kenmotsu manifold admitting a quarter-symmetric metric connection for illustration. © 2016, Transilvania University of Brasov 1. All rights reserved.

Some characterizations of Kenmotsu manifolds admitting a quarter-symmetric metric connection

In this paper, a type of closed sets, called *-g-closed sets, is introduced and studied in an ideal topological space. The class of such sets is found to lie strictly between the class of all closed sets and that of generalized closed sets of Levine [5]. We give some applications of *-g-closed set and *-g-open set in connection with certain separation axioms. © 2015, University of Nis. All Rights Reserved.

Filomat

Certain new classes of generalized closed sets and their applications in ideal topological spaces

The idea of countable near paracompactness of a topological space, as a natural offshoot 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 characterizations, semi near normality is used for the investigation of countably nearly paracompact spaces.

Matematicki Vesnik

On countably nearly paracompact spaces

The present article deals with near metrizability, initiated in an earlier paper [7], with a new orientation and approach. The notions of nearly regular and uniform pseudo-bases are introduced and analogues of some results concerning metrizability and paracompactness are obtained for near metrizability and near paracompactness respectively via the proposed approach, suitably formulated. © AGT, UPV, 2014.

Near metrizability via a new approach

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 some new characterizations of near paracompactness and associated results

The purpose of this paper is to introduce the notion of near metrizability for topological spaces, which is strictly weaker than the concept of metrizability. A number of characterizations of nearly metrizable spaces is achieved here as analogues of the corresponding ones for metrizable spaces. It is seen that near metrizability is a natural idea vis-a-vis near paracompactness, playing the similar role as played by paracompactness with regard to metrizability. © AGT, UPV, 2013.

Concerning nearly metrizable spaces

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.© Soc. Paran. de Mat.

Boletim da Sociedade Paranaense de Matematica

On a type of generalized closed sets

In the present article, a class of sets, called G-semiclosed sets, which is a subclass of the class of semi-closed sets of Levine [7], is introduced and studied in a grill topological space (X, τ, G), where G is a grill on X. Two types of functions are then introduced which ultimately lead us to achieve a new decomposition of a continuous function.