On hα-Open Sets In Topological Spaces

Sahil Billawria; Irfan  Ahmed; Shallu  Sharma

doi:10.5269/bspm.78503

Sahil Billawria Department of Mathematics, University of Jammu https://orcid.org/0000-0002-5419-3480
Irfan Ahmed Department of Mathematics, University of Jammu https://orcid.org/0009-0008-0580-9227
Shallu Sharma Department of Mathematics, University of Jammu https://orcid.org/0000-0001-8179-0080

Resumen

In 2022, Abdullah et.al [10] introduced a new class of open sets in topological space called hα-open sets. In this paper, we have introduced and study topological properties of hα-interior, hα-interior points, hα-neighbourhood, hα-closure, hα-exterior, hα-limit points, hα-derived, hα-border, hα-frontier by using the concept of hα-open sets. Also, we have presented the notion of almost hα-continuous, hα-contra continuous, almost hα-contra continuous, and strongly hα-continuous functions. Some properties, counter examples and theorems are established. Furthermore, we have shown that every strongly hα-continuous function is continuous and the composition of an hα-continuous and a strongly hα-continuous function is hα-irresolute.

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