Regularity of conservative inductive limits
type: Item
instance of: scholarly article
title: Regularity of conservative inductive limits
zbMATH Open document ID: 0968.46001
DOI: 10.1155/S0161171299227056
author: Yanyan Li
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2001-09-03T00:00:00Z
full work available at URL: https://eudml.org/doc/48880
review text: Let \(E_1\subset E_2 \subset \cdots \) be a sequence of Hausdorff locally convex spaces equipped with topologies \(\tau_n\). The author considers a set of conditions under which the inductive limit \(\text{ind}E_n\) is a regular space. Let us call that \(\text{ind}E_n\) is quasi-regular, if any bounded set in \(\text{ind}E_n\) is bounded in some space \(E_n\), and call conservative if for any linear subspace \(F\) of \(\text{ind}E_n\), it holds \(\text{ind}(F\cap E_n,\tau_n)=(F, \tau)\). The results are Theorem. Any sequentially complete conservative \(\text{ind} E_n\) is quasi regular and if each space \(E_n\) is closed in \(\text{ind}E_n\) then \(\text{ind}E_n\) is regular.
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A30
zbMATH DE Number: 1417968
zbMATH Keywords: quasi-regular
zbMATH Keywords: locally convex spaces
zbMATH Keywords: inductive limit topology
MaRDI profile type: Publication
OpenAlex ID: W1990618341
description: scientific article; zbMATH DE number 1417968