Quasi-bounded sets
type: Item
instance of: scholarly article
title: Quasi-bounded sets
zbMATH Open document ID: 0745.46006
DOI: 10.1155/S0161171290000849
author: Yanyan Li
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/46684
review text: Summary: It is well-known that a set bounded in an inductive limit \(E=\mathrm{indlim} E_ n\) of Fréchet spaces is also bounded in some \(E_ n\) iff \(E\) is fast complete. In the case of arbitrary locally convex spaces \(E_ n\) every bounded set in a fast complete \(\mathrm{indlim} E_ n\) is quasi-bounded in some \(E_ n\), though it may not be bounded or even contained in ay \(E_ n\). Every bounded set is quasi-bounded. In a Fréchet space every quasi-bounded set is also bounded.
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A03
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 5646
zbMATH Keywords: regular inductive limit
zbMATH Keywords: inductive limit
zbMATH Keywords: fast complete
zbMATH Keywords: quasi-bounded set
zbMATH Keywords: bounded set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5646