On the ``three-space'' problem for locally quasi-convex topological groups
type: Item
instance of: scholarly article
title: On the ``three-space'' problem for locally quasi-convex topological groups
zbMATH Open document ID: 0955.22006
published in: Archiv der Mathematik
publication date: 2001-02-20T00:00:00Z
review text: The main result of this paper is the analogue for topological groups of a theorem due to S.~Dierolf which states that there exists a nonlocally convex twisted sum of the locally convex spaces \(X\) and \(Y\) if and only if there exists a nonlocally convex twisted sum of \(X\) and \(\mathbb R\). It reads as follows: Given two abelian locally quasi-convex groups \(H\) and \(G\) there exists a nonlocally quasi-convex extension of \(H\) and \(G\) if and only if there exists a nonlocally quasi-convex extension of the circle group \(S^1\) and \(G\). The proof relies on methods of homological algebra.
reviewed by: Dirk Werner
Mathematics Subject Classification ID: 22B05
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46B08
zbMATH DE Number: 1462953
zbMATH Keywords: three-space problem
zbMATH Keywords: locally quasi-convex topological group
author: Jesús M. F. Castillo
MaRDI profile type: Publication
full work available at URL: s000130050439
OpenAlex ID: W2062532551
DOI: 10.1007/S000130050439
description: scientific article; zbMATH DE number 1462953