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http://hdl.handle.net/11320/6292
Tytuł: | F. Riesz Theorem |
Autorzy: | Narita, Keiko Nakasho, Kazuhisa Shidama, Yasunari |
Słowa kluczowe: | F. Riesz theorem dual spaces continuous functions |
Data wydania: | 2017 |
Data dodania: | 8-lut-2018 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 25, Issue 3, Pages 179–184 |
Abstrakt: | SummaryIn this article, we formalize in the Mizar system [1, 4] the F. Riesz theorem. In the first section, we defined Mizar functor ClstoCmp, compact topological spaces as closed interval subset of real numbers. Then using the former definition and referring to the article [10] and the article [5], we defined the normed spaces of continuous functions on closed interval subset of real numbers, and defined the normed spaces of bounded functions on closed interval subset of real numbers. We also proved some related properties.In Sec.2, we proved some lemmas for the proof of F. Riesz theorem. In Sec.3, we proved F. Riesz theorem, about the dual space of the space of continuous functions on closed interval subset of real numbers, finally. We applied Hahn-Banach theorem (36) in [7], to the proof of the last theorem. For the description of theorems of this section, we also referred to the article [8] and the article [6]. These formalizations are based on [2], [3], [9], and [11]. |
Afiliacja: | Narita Keiko - Hirosaki-city, Aomori, Japan Nakasho Kazuhisa - Akita Prefectural University, Akita, Japan Shidama Yasunari - Shinshu University, Nagano, Japan |
URI: | http://hdl.handle.net/11320/6292 |
DOI: | 10.1515/forma-2017-0017 |
ISSN: | 1426-2630 |
e-ISSN: | 1898-9934 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2017, Volume 25, Issue 3 |
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