<abstract xmlns="http://www.w3.org/1999/xhtml">Aspace <italic>X</italic> is said to have the absolutely strongly star -𝒤-Hurewicz (ASS𝒤H) property if for each sequence (𝒰<italic>n</italic> : <italic>n</italic> ∈ 𝕅)of opencovers of <italic>X</italic> and each dense subset <italic>Y</italic> of <italic>X</italic>, there is a sequence (<italic>Fn</italic> : <italic>n</italic> ∈ 𝕅) of finite subsets of <italic>Y</italic> such that for each <italic>x</italic> ∈ <italic>X</italic>, {<italic>n</italic> ∈ 𝕅 : <italic>x</italic> ∉ St(<italic>Fn</italic>, 𝒰<italic>n</italic>)}∈ 𝒤, where 𝒤 is the proper admissible ideal of 𝕅. In this paper, we investigate the relationship between the ASS𝒤H property and other related properties and study the topological properties of the ASS𝒤H property. This paper generalizes several results of Song [25] to the larger class of spaces having the ASS𝒤H properties.</abstract>

Aspace X is said to have the absolutely strongly star -𝒤-Hurewicz (ASS𝒤H) property if for each sequence (𝒰n : n ∈ 𝕅)of opencovers of X and each dense subset Y of X, there is a sequence (Fn : n ∈ 𝕅) of finite subsets of Y such that for each x ∈ X, {n ∈ 𝕅 : x ∉ St(Fn, 𝒰n)}∈ 𝒤, where 𝒤 is the proper admissible ideal of 𝕅. In this paper, we investigate the relationship between the ASS𝒤H property and other related properties and study the topological properties of the ASS𝒤H property. This paper generalizes several results of Song [25] to the larger class of spaces having the ASS𝒤H properties.

The Absolutely Strongly Star-Hurewicz Property with Respect to an Ideal

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Absolutely Strongly Star-Hurewicz Property with Respect to an Ideal"}

Aspace X is said to have the absolutely strongly star -𝒤-Hurewicz (ASS𝒤H) property if for each sequence (𝒰n : n ∈ 𝕅)of opencovers of X and each dense...

The Absolutely Strongly Star-Hurewicz Property with Respect to an Ideal

Published Online: Nov 04, 2020

Page range: 81 - 94

Received: Mar 27, 2020

DOI: https://doi.org/10.2478/tmmp-2020-0020

Keywords
Hurewicz, absolutely strongly star-Hurewicz, strongly star-Hurewicz, Menger, absolutely strongly star-Menger, strongly star-Menger, covering, ideal, topological space

© 2020 Sumit Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Absolutely Strongly Star-Hurewicz Property with Respect to an Ideal

Published Online: Nov 04, 2020

Page range: 81 - 94

Received: Mar 27, 2020

DOI: https://doi.org/10.2478/tmmp-2020-0020

KeywordsHurewicz, absolutely strongly star-Hurewicz, strongly star-Hurewicz, Menger, absolutely strongly star-Menger, strongly star-Menger, covering, ideal, topological space

© 2020 Sumit Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Hurewicz, absolutely strongly star-Hurewicz, strongly star-Hurewicz, Menger, absolutely strongly star-Menger, strongly star-Menger, covering, ideal, topological space