Fréchetness of inverse limits and products
type: Item
instance of: scholarly article
title: Fréchetness of inverse limits and products
zbMATH Open document ID: 0605.54019
DOI: 10.1016/0166-8641(85)90035-5
author: T. Nogura
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: A class \({\mathcal C}\) of spaces is almost countably productive provided that for every sequence \(\{X_ n\}\) of spaces, the product of all the \(X_ n\) is in \({\mathcal C}\) whenever each finite product of the \(X_ n\) is in \({\mathcal C}\). Furthermore \({\mathcal C}\) is countably projective provided that the inverse limit is in \({\mathcal C}\) for each inverse sequence from \({\mathcal C}\) with surjective bonding maps. The latter implies the former. This paper shows that each of the six classes of spaces \(<\alpha_ 1>\), \(<\alpha_ 2>\), \(<\alpha_ 3>\), \(<\alpha_ 1-FU>\), \(<\alpha_ 2-FU>\) and \(<\alpha_ 3-FU>\) [due to \textit{A. V. Arkhangel'skij}, Dokl. Akad. Nauk SSSR 206, 265-268 (1972; Zbl 0275.54004)] is countably projective. Here \(<\alpha_ i-FU>\) stands for the intersection of \(<\alpha_ i>\) and the class of Fréchet-Urysohn spaces. The class \(<\alpha_ 2>\) is precisely the class of w-spaces. So this answers a question of Galvin as to whether the class of w-spaces is countably productive.
Mathematics Subject Classification ID: 54D55
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54B35
zbMATH DE Number: 3977907
zbMATH Keywords: (almost) countably productive class
zbMATH Keywords: class of Fréchet-Urysohn spaces
zbMATH Keywords: class of w-spaces
reviewed by: R. A. McCoy
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90035-5
OpenAlex ID: W2034296584
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description: scientific article; zbMATH DE number 3977907