The open-point and bi-point-open topologies on C(X)

被引：8

作者：

Jindal, Anubha ^{[1
]}

McCoy, R. A. ^{[2
]}

Kundu, S. ^{[1
]}

机构：

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

[2] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

来源：

TOPOLOGY AND ITS APPLICATIONS | 2015年 / 187卷

关键词：

Point-open topology; Open-point topology; Bi-point-open topology; Zero-set; G(delta)-dense; Separation; Topological group; Metrizable; First countable; Separable; Second countable; Lindelof;

D O I：

10.1016/j.topol.2015.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the definition of a set-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X, we use a certain family of subsets of X and open subsets of R. But instead of using this traditional way to define topologies on in this paper, we adopt a different approach to define two interesting topologies on C(X). We call them the open-point and the bi-point-open topologies and study the separation and countability properties of these topologies. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：62 / 74

页数：13

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