The compact-open topology: A new perspective

被引：5

作者：

Kundu, S. ^{[2
]}

Garg, Pratibha ^{[1
]}

机构：

[1] Thapar Univ, Sch Math & Comp Applicat, Patiala 147004, Punjab, India

[2] Indian Inst Technol, Dept Math, New Delhi 110016, India

来源：

TOPOLOGY AND ITS APPLICATIONS | 2009年 / 156卷 / 04期

关键词：

Function space; Metrizable; Completely metrizable; Cech-complete; Sieve-complete; Partition-complete; Baire space; Barreled; Separable; Second countable; TRI-QUOTIENT MAPS; COMPLETE SPACES; COMPLETENESS;

D O I：

10.1016/j.topol.2008.09.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the compact-open topology on the set KC(X) of all real-valued functions defined on a Tychonoff space, which are continuous on compact subsets of X. In addition to metrizability. separability and second countability, of this topology on KC(X), various kinds of topological properties of this topology are studied in detail. Actually the motivation for studying the compact-open topology on KC(X) lies in the attempt of having a simpler proof for the characterization of a completeness property of the compact-open topology on C(X), the set of all real-valued continuous functions on X (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：686 / 696

页数：11

共 25 条

[1] The metrizability and completeness of the σ-compact-open topology on C*(X)
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[2] Cech-completeness and related properties of the generalized compact-open topology
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[4] On selective sequential separability of function spaces with the compact-open topology
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[7] Topological and functional analytic properties of the compact-Gδ-open topology on C(X)
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[8] The metrizability and completeness of the support-open topology on C(X)
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[9] THE CLP-COMPACT-OPEN TOPOLOGY ON KC(X, Y)
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JOURNAL OF SCIENCE AND ARTS, 2022, (01) : 55 - 62
[10] Completeness properties of the pseudocompact-open topology on C(X)
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