Closed maps on spaces with point-countable bases
type: Item
instance of: scholarly article
title: Closed maps on spaces with point-countable bases
zbMATH Open document ID: 0952.54002
DOI: 10.1016/S0166-8641(98)00013-3
published in: Topology and its Applications
publication date: 2001-01-10T00:00:00Z
review text: The structure of spaces which are closed images of (regular) spaces with point-countable bases is studied. The author shows that such spaces have countable \(\pi\)-character and a point-countable \(\pi\)-base and consequently topological groups of that kind are metrizable. He also obtains a theorem which is one more generalization of Lashnev's well-known theorem concerning closed mappings on metric spaces.
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54D55
zbMATH DE Number: 1340405
zbMATH Keywords: point-countable base
zbMATH Keywords: closed map
zbMATH Keywords: Lashnev's theorem
zbMATH Keywords: sequential order
zbMATH Keywords: \(\pi\)-base
zbMATH Keywords: \(\pi\)-character
author: Alexander Y. Shibakov
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1340405