Mapping theorems on \(\aleph\)-spaces
type: Item
instance of: scholarly article
title: Mapping theorems on \(\aleph\)-spaces
zbMATH Open document ID: 0663.54017
DOI: 10.1016/0166-8641(88)90014-4
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: The following results are proved: Theorem: \(\aleph\)-spaces (i.e. regular spaces with a \(\sigma\)-locally finite \(\kappa\)-network) are pressed by closed Lindelöf continuous maps (f: \(X\to Y\) is Lindelöf if \(f^{- 1}(y)\) is Lindelöf for each \(y\in Y)\). Theorem. A perfect inverse image of an \(\aleph\)-space is an \(\aleph\)-space iff it has a \(G_{\delta}\)- diagonal or a point-countable \(\kappa\)-network.
Mathematics Subject Classification ID: 54E18
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54D55
zbMATH DE Number: 4084545
zbMATH Keywords: Fréchet space
zbMATH Keywords: Lashnev space
zbMATH Keywords: compact-covering mapping
zbMATH Keywords: perfect mapping
zbMATH Keywords: \(\aleph \)-spaces
zbMATH Keywords: closed Lindelöf continuous maps
zbMATH Keywords: \(G_{\delta }\)-diagonal
zbMATH Keywords: point-countable \(\kappa\)-network
author: Shou Lin
reviewed by: Carlos R. Borges
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90014-4
OpenAlex ID: W2091497410
cites work: Characterizations of \(\aleph\)-spaces
cites work: A Characterization of Closed Images of Metric Spaces
cites work: Q4185451
cites work: Spaces determined by point-countable covers
cites work: Q5526599
cites work: A Characterization for the Products of k-and- ℵ 0 -Spaces and Related Results
description: scientific article; zbMATH DE number 4084545