On Characterization of b-Open Sets in Cofinite Topology on R

On Characterization of b-Open Sets in Cofinite Topology on R

Dwaipayan Mishra, Himadri Shekhar Mondal, Motahar Reza, Amalendu Rana
Copyright: © 2023 |Pages: 8
DOI: 10.4018/978-1-6684-7343-6.ch014
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Abstract

In this article, the characterization of different types of open sets in cofinite topology on the set of real numbers has been carved. Here specially b-open sets in the cofinite topology has been studied. The authors have characterized the b-open sets in the cofinite topology over R where one characterization facilitates to apprehend a group of sets to be b open and an other group of sets not to be b-open in the cofinite topology on the set of real numbers spontaneously. Furthermore, some important results on these sets are investigated and proved.
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Basic Definitions

Semi-Open Set

Let (U,𝜏) be a topological space. A subset X of the topological space U is said to be semi-open set (Andrijevic, 1986; Levine, 1963; Mashhour et al., 1982) if 978-1-6684-7343-6.ch014.m05.

  • Example-1: Let978-1-6684-7343-6.ch014.m06 is a topological space on the set of Real numbers 978-1-6684-7343-6.ch014.m07 with the usual topology. Then,

    • (i)

      An open set in 978-1-6684-7343-6.ch014.m08 is a semi open set.

    • (ii)

      A closed interval in 978-1-6684-7343-6.ch014.m09 is semi open set in978-1-6684-7343-6.ch014.m10.

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