Bounded nets in preseminormed spaces
type: Item
instance of: scholarly article
title: Bounded nets in preseminormed spaces
zbMATH Open document ID: 0776.46006
DOI: 10.1007/BF02278035
published in: Periodica Mathematica Hungarica
publication date: 1992-09-27T00:00:00Z
review text: By using preseminormed spaces instead of topological vector spaces, we introduce a reasonable new notion of bounded nets under which each Cauchy net becomes bounded. And after some preparations, we show that bounded nets and null nets can be characterized in terms of each other. Moreover, by identifying sets with nets in a natural way, we obtain standard theorems on bounded sets as very particular cases of our results.
Mathematics Subject Classification ID: 46A19
Mathematics Subject Classification ID: 46A16
zbMATH DE Number: 60712
zbMATH Keywords: preseminormed spaces
zbMATH Keywords: bounded nets
zbMATH Keywords: Cauchy net
zbMATH Keywords: null nets
author: Árpád Száz
MaRDI profile type: Publication
cites work: Q5667036
cites work: Q3346792
cites work: Q3496760
cites work: Q3730422
cites work: Q4178057
description: scientific article; zbMATH DE number 60712