Uniform continuity in sequentially uniform spaces
type: Item
instance of: scholarly article
title: Uniform continuity in sequentially uniform spaces
zbMATH Open document ID: 0819.54014
DOI: 10.1007/BF01872093
published in: Acta Mathematica Hungarica
publication date: 1994-09-05T00:00:00Z
review text: The authors prove that every uniformly sequential uniform space is proximally fine, i.e., it is the finest uniform space inducing its proximity (no references to this result are given; it was proved e.g. by \textit{N. S. Ramm} and \textit{A. S. Shvarts} [Mat. Sb., Nov. Ser. 33(75), 157-180 (1952; Zbl 0050.391)]). Two consequences are given describing when a uniformly sequential space is topologically fine (both consequences, except the fourth condition in the second one, are valid for any proximally fine space).
Mathematics Subject Classification ID: 54E15
zbMATH DE Number: 633878
zbMATH Keywords: uniformly sequential space
zbMATH Keywords: proximally fine space
author: Anna Di Concilio
author: S. Naimpally
reviewed by: M. Hušek
MaRDI profile type: Publication
cites work: Uniform continuity of continuous functions of metric spaces
cites work: Metric Spaces on which Continuous Functions are Uniformly Continuous and Hausdorff Distance
description: scientific article; zbMATH DE number 633878