On mappings from products into developable spaces
type: Item
instance of: scholarly article
title: On mappings from products into developable spaces
zbMATH Open document ID: 0632.54006
DOI: 10.1016/0166-8641(87)90043-5
author: Harald Brandenburg
author: M. Hušek
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: A topological space is subnormal, respectively D-normal, if every pair of disjoint closed subsets can be separated by \(G_{\delta}\)-sets, respectively closed \(G_{\delta}\)-sets. This interesting paper addresses the problem as to whether there exists, for every non-compact Hausdorff space X, a cardinal \(\kappa\) such that \(^{\kappa}X\) is not subnormal, and gives the partial answer that \(^{\kappa}X\) is not D-normal whenever \(\kappa \geq \max (\omega_ 1,w(X))\), where w(X) is the weight of X. The proof involves the use of a characterization of continuous mappings from a product into a developable \(T_ 1\)-space, depending on countably many coordinates, and the whole leans on work of \textit{N. Noble} [Trans. Am. Math. Soc. 160, 169-183 (1971; Zbl 0233.54004)] and \textit{J. Keesling} [Adv. Math. 9, 90-92 (1972; Zbl 0243.54003)]. Some open problems are noted.
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 54E30
Mathematics Subject Classification ID: 54D15
zbMATH DE Number: 4028375
zbMATH Keywords: developable space
zbMATH Keywords: subdevelopable space
zbMATH Keywords: subparacompact space
zbMATH Keywords: perfect space
zbMATH Keywords: D-normal space
zbMATH Keywords: subnormal space
zbMATH Keywords: D-closed set
zbMATH Keywords: mapping depending on countably many coordinates
zbMATH Keywords: developable \(T_ 1\)-space
reviewed by: Pieter Collins
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90043-5
OpenAlex ID: W1984382242
cites work: Metrization of Topological Spaces
cites work: Separating Closed Sets by Continuous Mappings into Developable Spaces
cites work: An extension theorem for D-normal spaces
cites work: On D-paracompact spaces
cites work: On subparacompactness and related properties
cites work: On d-paracompactness and related properties
cites work: Normality in Subsets of Product Spaces
cites work: Q3900646
cites work: Normality of Powers Implies Compactness
cites work: The Category of D-Completely Regular Spaces is Simple
cites work: Algebra ∩ topology = compactness
cites work: Q4151370
cites work: Normality and infinite product spaces
cites work: A note on countably subparacompact spaces
cites work: Products with Closed Projections. II
cites work: Factoring Functions on Cartesian Products
cites work: Moore Spaces, Semi-Metric Spaces and Continuous Mappings Connected with Them
cites work: Remarks on Cartesian products
cites work: On N. Noble's theorems concerning powers of spaces and mappings
cites work: Metrization of Moore spaces and generalized manifolds
cites work: REAL FUNCTIONS AND CANONICAL SETS IN TIKHONOV PRODUCTS AND TOPOLOGICAL GROUPS
cites work: Q3959097
cites work: Q3878381
cites work: Paracompactness and product spaces
cites work: Point-Countability and Compactness
description: scientific article; zbMATH DE number 4028375