Connectedness via (1, 2)Sβ - open sets in Bitopological spaces

Jeyanthi P.; Subprabha Visveswaraiah; Durga Devi  Natarajan; Jafari  Syed

doi:10.5269/bspm.78443

Jeyanthi P. Principal, (Retired) Govindammal Aditanar College for Women,Tiruchendur, 628 214Tamil nadu, India
V. Subprabha Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628215 Tamilnadu, India. https://orcid.org/0009-0006-0740-4456
N. Durga Devi Department of Mathematics, Sri Parasakthi College for Women (Autonomous), Courtallam, Tenkasi-627 802 Tamilnadu, India. https://orcid.org/0009-0002-2147-593X
S. Jafari Mathematical and Physical Science Foundation, 4200 Slagelse, Denmark. https://orcid.org/0000-0001-5744-7354

Abstract

Topology is a fundamental branch of mathematics thar provides a framework for studying spaces
and their properties. Central to topology is the concept of open sets, which are subsets of a given space defined by specific characteristics inherent to the spaces structure. These open sets form the foundation for various topological properties, allowing for a deeper understanding of connectivity within the space. In this work, we introduce a class of open sets in bitopological spaces namely (1, 2)S_β - open set by involving (1, 2) semi- open set and (1, 2)_β -closed set. In addition, we present the essential properties of this class and study its relationship with the other classes of open sets with the help of counter examples. Further, we introduce (1, 2)S_β - separated sets, (1, 2)S_β - connected sets and study their properties in bitopological spaces. Also, we
prove some results related to (1, 2)S_β - continuous functions.

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Author Biographies

Jeyanthi P., Principal, (Retired) Govindammal Aditanar College for Women,Tiruchendur, 628 214Tamil nadu, India

Head of the Department of Mathematics

V. Subprabha, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628215 Tamilnadu, India.

Assistant Professor

N. Durga Devi, Department of Mathematics, Sri Parasakthi College for Women (Autonomous), Courtallam, Tenkasi-627 802 Tamilnadu, India.

Assistant Professor

S. Jafari, Mathematical and Physical Science Foundation, 4200 Slagelse, Denmark.

Professor

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