Functional Space Consisted by Continuous Functions on Topological Space

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...

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Bibliographic Details
Published in:	Formalized Mathematics Vol. 29; no. 1; pp. 49 - 62
Main Authors:	Yamazaki, Hiroshi, Miyajima, Keiichi, Shidama, Yasunari
Format:	Journal Article
Language:	English Japanese
Published:	Bialystok Walter de Gruyter GmbH 01.04.2021 Sciendo De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:	46E10 68V20 Banach space compact topological space continuous function space
ISSN:	1898-9934, 1426-2630, 1898-9934
Online Access:	Get full text
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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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1898-9934 1426-2630 1898-9934
DOI:	10.2478/forma-2021-0005