Some observations on Hurewicz and \(\mathcal{I}\)-Hurewicz property
type: Item
instance of: scholarly article
title: Some observations on Hurewicz and \(\mathcal{I}\)-Hurewicz property
zbMATH Open document ID: 1416.54009
author: Pratulananda Das
author: Upasana Samanta
author: Debraj Chandra
published in: Topology and its Applications
publication date: 2019-04-24T00:00:00Z
review text: In this paper the authors study some observations on the Hurewicz and the $\mathcal{I}$-Hurewicz property. We know that the ideal variant of the Hurewicz property, the $\mathcal{I}$-Hurewicz property was introduced and studied by \textit{P. Das} [Houston J. Math. 39, No. 2, 637--650 (2013; Zbl 1273.54022)] (later in [\textit{P. Das} et al., Topology Appl. 202, 183--193 (2016; Zbl 1337.54010)]). The $\mathcal{I}$-Hurewicz property defined here is the $\mathcal{F}$-Menger property [\textit{T. Banakh} et al., Topology Appl. 157, No. 2, 466--481 (2010; Zbl 1184.54033)] and a more general version called $\mathcal{S}$-Menger property has been recently studied in [\textit{P. Szewczak} and \textit{B. Tsaban}, Ann. Pure Appl. Logic 168, No. 1, 1--18 (2017; Zbl 1355.54026)]. In Sections 3.1, 3.2, 3.3 and 3.4, the authors give interesting results concering the Hurewicz and the $\mathcal{I}$-Hurewicz property using selection principles and preservation of the $\mathcal{I}$-Hurewicz property. Finally, in Section 3.5 they present observations on the $\mathcal{I}$-Hurewicz property in certain special structures.
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 7047518
zbMATH Keywords: ideal
zbMATH Keywords: filter
zbMATH Keywords: semi-filter
zbMATH Keywords: \(\mathcal{I}\)-bounded
zbMATH Keywords: Hurewicz property
zbMATH Keywords: \(\mathcal{I}\)-Hurewicz property
zbMATH Keywords: \(\mathcal{I}\)-\(\gamma\)-cover
zbMATH Keywords: \(\mathcal{I}\)-groupable open cover
zbMATH Keywords: large cover
reviewed by: Dimitris Georgiou
MaRDI profile type: Publication
full work available at URL: j.topol.2019.01.015
OpenAlex ID: W2912645570
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DOI: 10.1016/J.TOPOL.2019.01.015
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description: scientific article; zbMATH DE number 7047518