On Almost and Star α-Hurewicz Spaces

Authors

  • Tamadher Waleed Said Ghani Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq. https://orcid.org/0009-0004-5285-3133
  • Jalal Hatem Hussein Bayati Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq. https://orcid.org/0000-0002-3070-2391
  • Ana María Zarco Department of Mathematics, Universidad Internacional de La Rioja, Logroño, Spain.

DOI:

https://doi.org/10.22401/avvpbn36

Keywords:

Almost α-Hurewicz, Almost star α-Hurewicz, α-Compact space, α-Hurewicz space, α-Lindelof space, α-Open cover, Star α-Hurewicz

Abstract

The main purpose of this work is to create a type of topological spaces namely "almost star α-Hurewicz spaces" and study its properties, and besides, the concepts of α-compact space, α-Hurewicz space, star α-Hurewicz space and strongly star α-Hurewicz space. Many properties of α-Hurewicz spaces and almost α-Hurewicz are investigated. This allows us to provide new examples of explicit descriptions of spaces as well as some types of α-covering for spaces such as α-compact and α-Lindelof space and using as a tool to prove important results in topological spaces. In addition, a certain connection of α-Hurewicz space with the Hurewicz space and almost α-Hurewicz space was considered. There is a relationship between the version of the strongly star α-Hurewicz property and star α-Hurewicz property with star α-compact property and almost star α-Hurewicz. Some of the examples that make a distinction between the properties are mentioned and reviewed, showing that the concepts are not equivalent. Results on the preservation of the properties of α-Hurewicz and almost-α-Hurewicz spaces are included such as behavior under subspaces, products, α-irresolute function, and mappings with other forms of topological spaces.

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Published

2024-09-16

How to Cite

(1)
On Almost and Star α-Hurewicz Spaces. ANJS 2024, 27 (3), 142-148. https://doi.org/10.22401/avvpbn36.