拓扑空间上由连续函数组成的泛函空间

IF 1 Q1 MATHEMATICS

Formalized Mathematics Pub Date : 2021-04-01 DOI:10.2478/forma-2021-0005

Hiroshi Yamazaki, K. Miyajima, Y. Shidama

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引用次数: 1

摘要

本文利用Mizar系统[1]，[2]，首先给出了由紧拓扑空间上定义的所有连续函数构成的泛函空间的定义[5]。我们证明了这个泛函空间是一个Banach空间[3]。其次，给出了由所有具有有界支持的连续函数构成的函数空间的定义。我们也证明了这个函数空间是赋范空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Functional Space Consisted by Continuous Functions on Topological Space

Summary In this article, using the Mizar system [1], [2], first we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space [5]. We prove that this functional space is a Banach space [3]. Next, we give a definition of a function space which is constructed from all continuous functions with bounded support. We also prove that this function space is a normed space.

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来源期刊

Formalized Mathematics MATHEMATICS-

自引率

0.00%

发文量

审稿时长

10 weeks

期刊介绍： Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.