Hereditary screenableness and its Tychonoff products
type: Item
instance of: scholarly article
title: Hereditary screenableness and its Tychonoff products
zbMATH Open document ID: 0924.54030
DOI: 10.1016/S0166-8641(97)00111-9
published in: Topology and its Applications
publication date: 1999-11-08T00:00:00Z
review text: It is known that a space \(X\) is hereditarily metacompact (metalindelöf) iff every scattered partition of \(X\) has a point-finite (point-countable) open expansion. The author observes that similar reasonings lead to a characterization of hereditarily screenable spaces and he uses this characterization to obtain some product theorems for hereditarily screenable spaces. Reviewer's remark: The proper references to the results cited in the first paragraph of the review are: Proposition 3.8 in [\textit{H. J. K. Junnila}, in `Surveys in general topology', 195-245 (1980; Zbl 0449.54018)] and Theorem 8.1 in [\textit{G. Gruenhage, E. Michael} and \textit{Y. Tanaka}, Pac. J. Math. 113, 303-332 (1984; Zbl 0561.54016)].
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54E18
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 1308039
zbMATH Keywords: hereditarily screenable
zbMATH Keywords: scattered partition
author: Peiyong Zhu
reviewed by: Jozef Chaber
MaRDI profile type: Publication
cites work: Closure-preserving covers by small sets
cites work: Q3685653
cites work: Q4150804
cites work: Some results about covering properties of products
cites work: Q4326513
Wikidata QID: Q127125279
description: scientific article; zbMATH DE number 1308039