# International Journal of Pure Mathematics

**E-**ISSN: 2313-0571

Volume 8, 2021

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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**Volume 8, 2021**

**Title of the Paper:** Infra -α- Compact and Infra -α- Connected Spaces

**Authors:** Raja Mohammad Latif

**Pages: **41-57

**DOI:**** **10.46300/91019.2021.8.6 **XML**

**Abstract:** In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, countably infra -α- compact space, infra -α- Lindelof space, almost infra -α- compact space, mildly infra -α- compact space and infra -α- connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.

**Title of the Paper:** On Fuzzy L-paracompact Topological Spaces

**Authors:** Francisco Gallego Lupiáñez

**Pages: **38-40

**DOI:**** **10.46300/91019.2021.8.5 **XML**

**Abstract:** The aim of this paper is to study fuzzy extensions of some covering properties defined by L. Kalantan as a modification of some kinds of paracompactness-type properties due to A.V.Arhangels'skii and studied later by other authors. In fact, we obtain that: if (X,T) is a topological space and A is a subset of X, then A is Lindelöf in (X,T) if and only if its characteristic map χ_{A} is a Lindelöf subset in (X,ω(T)). If (X,τ) is a fuzzy topological space, then, (X,τ) is fuzzy Lparacompact if and only if (X,ι(τ)) is L-paracompact, i.e. fuzzy L-paracompactness is a good extension of L-paracompactness. Fuzzy L₂-paracompactness is a good extension of L₂- paracompactness. Every fuzzy Hausdorff topological space (in the Srivastava, Lal and Srivastava' or in the Wagner and McLean' sense) which is fuzzy locally compact (in the Kudri and Wagner' sense) is fuzzy L₂-paracompact

**Title of the Paper:** Table Algebra of Infinite Tables, Multiset Table Algebra, and their Relationship

**Authors:** Iryna Lysenko

**Pages: **34-37

**DOI:**** **10.46300/91019.2021.8.4 **XML**

**Abstract:** The paper is focused on some theoretical questions of the table databases. Two mathematical formalisms such as table algebra of infinite tables and multiset table algebra are considered. Basic definitions referring to these formalisms are given. This paper also addresses the issue of the relationship between table algebra of infinite tables and multiset table algebra. It is proved that table algebra of infinite tables is not a subalgebra of multiset table algebra since it is not closed in relation to some signature operations of multiset table algebra. These signature operations are determined.

**Title of the Paper:** Cartesian Product and Topology on Fuzzy BI-Algebras

**Authors:** Gerima Tefera, Abdi Oli

**Pages: **29-33

**DOI:**** **10.46300/91019.2021.8.3 **XML**

**Abstract:** In this paper, the concepts of homomorphism in fuzzy BI-algebra is intro- duced, and also basic properties of homo- morphisms are investigated. The cartesian product in fuzzy ideals of BI-algebra is investigated with related prop- erties; The concepts of fuzzy topology on BI- algebra elaborated.

**Title of the Paper:** Closed Analytic Formulas for the Approximation of the Legendre Complete Elliptic Integrals of the First and Second Kinds

**Authors:** Richard Selescu

**Pages: **23-28

**DOI:**** **10.46300/91019.2021.8.2 **XML**

**Abstract:** The author proposes two sets of closed analytic functions for the approximate calculus of the complete elliptic integrals of the first and second kinds in the normal form due to Legendre, the respective expressions having a remarkable simplicity and accuracy. The special usefulness of the proposed formulas consists in that they allow performing the analytic study of variation of the functions in which they appear, by using the derivatives. Comparative tables including the approximate values obtained by applying the two sets of formulas and the exact values, reproduced from special functions tables are given (all versus the respective elliptic integrals modulus, k = sin θ). It is to be noticed that both sets of approximate formulas are given neither by spline nor by regression functions, but by asymptotic expansions, the identity with the exact functions being accomplished for the left end k = 0 (θ = 0°) of the domain. As one can see, the second set of functions, although something more intricate, gives more accurate values than the first one and extends itself more closely to the right end k = 1 (θ= 90°) of the domain. For reasons of accuracy, it is recommended to use the first set until θ = 70°.5 only, and if it is necessary a better accuracy or a greater upper limit of the validity domain, to use the second set, but on no account beyond θ = 88°.2.

**Title of the Paper:** Delta – Open Sets and Delta – Continuous Functions

**Authors:** Raja Mohammad Latif

**Pages: **1-22

**DOI:**** **10.46300/91019.2021.8.1 **XML**

**Abstract:** In 1968 Velicko [30] introduced the concepts of δ-closure and δ-interior operations. We introduce and study properties of δ-derived, δ-border, δ-frontier and δ-exterior of a set using the concept of δ-open sets. We also introduce some new classes of topological spaces in terms of the concept of δ-D- sets and investigate some of their fundamental properties. Moreover, we investigate and study some further properties of the well-known notions of δ-closure and δ-interior of a set in a topological space. We also introduce δ-R0 space and study its characteristics. We also introduce δ-R0 space and study its characteristics. We introduce δ-irresolute, δ-closed, pre-δ-open and pre -δ-closed mappings and investigate properties and characterizations of these new types of mappings and also explore further properties of the well-known notions of δ-continuous and δ-open mappings.