Some Variants of Strong Normality in Closure Spaces Generated via Relations

Journal of Mathematics ◽

10.1155/2021/6917297 ◽

2021 ◽

Vol 2021 ◽

pp. 1-7

Author(s):

Ria Gupta ◽

Ananga Kumar Das

Keyword(s):

Binary Relation ◽

Normal Closure ◽

Separation Axioms ◽

Closure Spaces ◽

Strong Normality

In this paper, some variants of strongly normal closure spaces obtained by using binary relation are introduced, and examples in support of existence of the variants are provided by using graphs. The relationships that exist between variants of strongly normal closure spaces and covering axioms in absence/presence of lower separation axioms are investigated. Further, closure subspaces and preservation of the properties studied under mapping are also discussed.

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On normality of a closure space generated from a tree by relation

Asian-European Journal of Mathematics ◽

10.1142/s1793557122501108 ◽

2021 ◽

pp. 2250110

Author(s):

A. K. Das ◽

Ria Gupta

Keyword(s):

Comparative Study ◽

Binary Relation ◽

Applied Mathematics ◽

Closure Space ◽

Topological Properties ◽

Closure Spaces

Binary relation plays a prominent role in the study of mathematics in particular applied mathematics. Recently, some authors generated closure spaces through relation and made a comparative study of topological properties in the space by varying the property on the relation. In this paper, we have studied closure spaces generated from a tree through binary relation and observed that under certain situation the space generated from a tree is normal.

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Some higher separation axioms in soft Cech closure spaces

International Mathematical Forum ◽

10.12988/imf.2015.5646 ◽

2015 ◽

Vol 10 ◽

pp. 519-525

Author(s):

R. Gowri ◽

G. Jegadeesan

Keyword(s):

Separation Axioms ◽

Closure Spaces

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Minimal structure approximation space and some of its application

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201090 ◽

2021 ◽

Vol 40 (1) ◽

pp. 973-982

Author(s):

M. M. El-Sharkasy

Keyword(s):

Information System ◽

Binary Relation ◽

Real Life ◽

Approximation Space ◽

Generalized System ◽

Separation Axioms ◽

Life Problems ◽

Minimal Structure ◽

Starting Point ◽

New Space

Topological concepts play an important role in applications and solving real-life problems. Among of these concepts are neighbourhood and minimal structure. In this paper, we introduce a new space-based on a generalized system with a binary relation on a nonempty set by using the concept of a minimal structure, which is called a minimal structure approximation space (briefly, MSAS), and study some of its properties. Also, we compare the advantages of MSAS with neighbourhood approximation space which are based on the same starting point, and apply the concept of MSAS in some examples of chemistry to extraction and reduct the information. Finally, we investigate the concepts of the separation axioms on MSAS and study some of its properties in the information system as the process of approximation of information.

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