Original scientific paper

Operation approach to ß-open sets and applications

Sanjay Tahiliani ; Department of Mathematics, Delhi University, Delhi, India

Abstract

In this paper, we introduce the concept of an operation $\gamma$
on a family of $\beta$-open sets denoted by $\beta O(X)$ in a topological space $(X,\tau)$.
Using the operation $\gamma$ on $\beta O(X)$, we introduce the concept of $\beta$-$\gamma$-open sets, and investigate the related topological properties.
We also introduce the notion of $\beta$-$\gamma$-$T_{i}$ spaces $(i =0, 1/2, 1, 2)$ and study some topological properties on them. Further, we introduce $\beta$-$(\gamma, b)$-continuous maps and investigate basic properties.
Finally, we investigate a general operation approach to $\beta$-closed
graphs of mappings.

Keywords

$\beta$-$\gamma$-open set; $\beta$-$\gamma$-closure; $\beta O(X)_{\gamma}$-closure; $\beta$-$(\gamma; b)$-continuous

Hrčak ID:

74902

URI

https://hrcak.srce.hr/74902

Publication date:

21.12.2011.

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