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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Veröffentlicht in:Formalized Mathematics Jg. 29; H. 1; S. 49 - 62
Hauptverfasser: Yamazaki, Hiroshi, Miyajima, Keiichi, Shidama, Yasunari
Format: Journal Article
Sprache:Englisch
Japanisch
Veröffentlicht: Bialystok Walter de Gruyter GmbH 01.04.2021
Sciendo
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Schlagworte:
46E10
68V20
Banach space
compact topological space
continuous function space
ISSN:1898-9934, 1426-2630, 1898-9934
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
Bibliographie: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