Observations about equicontinuity and related concepts

被引：2

作者：

Corbacho, Eusebio ^{[1
]}

Tarieladze, Vaja ^{[2
]}

Vidal, Ricardo ^{[1
]}

机构：

[1] Univ Vigo, Dept Matemat Aplicada 1, Vigo, Spain

[2] Niko Muskhelishvili Inst Computat Math, GE-0171 Tbilisi, Georgia

来源：

TOPOLOGY AND ITS APPLICATIONS | 2009年 / 156卷 / 18期

关键词：

Equicontinuity; Even continuity; Topological equicontinuity; Compact equicontinuity; Ascoli theorem; Normed space; Weak topology;

D O I：

10.1016/j.topol.2009.02.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The concepts of equicontinuity, even continuity, topological equicontinuity and the newly defined concepts of compact equicontinuity and compact topological equicontinuity are compared. It is shown that for a set of group homomorphisms from a semitopological group to a topological group all these notions of equicontinuities coincide. It is shown also that an infinite-dimensional normed space endowed with its weak topology is an example of a space which does not satisfy the Ascoli theorem in Noble's sense. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：3062 / 3069

页数：8

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