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http://hdl.handle.net/11320/17772Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Miyajima, Keiichi | - |
| dc.contributor.author | Yamazaki, Hiroshi | - |
| dc.date.accessioned | 2025-01-03T09:15:01Z | - |
| dc.date.available | 2025-01-03T09:15:01Z | - |
| dc.date.issued | 2024 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 32, Issue 1, Pages 141–147 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/17772 | - |
| dc.description.abstract | We formulate and prove in Mizar the Ascoli-Arzel`a’s theorem, which gives necessary and sufficient conditions for a collection of continuous functions to be compact. We use the metric space setting, and the notions of equicontinuousness and equiboundedness of a set of continuous functions are utilized. | pl |
| dc.language.iso | en | pl |
| dc.publisher | DeGruyter Open | pl |
| dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
| dc.subject | Ascoli-Arzel`a theorem | pl |
| dc.subject | equicontinuousness of continuous functions | pl |
| dc.subject | equiboundedness of continuous functions | pl |
| dc.title | Ascoli-Arzel`a Theorem (Metric Space Version) | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2024 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2024-0011 | - |
| dc.description.Affiliation | Keiichi Miyajima - Ibaraki University, Faculty of Engineering, Hitachi, Ibaraki, Japan | pl |
| dc.description.Affiliation | Hiroshi Yamazaki - Nagano Prefectural Institute of Technology, Nagano, Japan | pl |
| dc.description.references | Cesare Arzel`a. Sulle funzioni di linee. Mem. Accad. Sci. Ist. Bologna Cl. Sci. Fis. Mat., 5(5):55–74, 1895. | pl |
| dc.description.references | Giulio Ascoli. Le curve limite di una variet`a data di curve. Atti della R. Accad. Dei Lincei Memorie della Cl. Sci. Fis. Mat. Nat., 18(3):521–586, 1883–1884. | pl |
| dc.description.references | Bruce K. Driver. Analysis Tools with Applications. Springer, Berlin, 2003. | pl |
| dc.description.references | John L. Kelley. General Topology, volume I, II. von Nostrand, 1955. | pl |
| dc.description.references | Serge Lang. Real and Functional Analysis (Texts in Mathematics). Springer-Verlag, 1993. | pl |
| dc.description.references | The mathlib Community. The Lean mathematical library. In Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2020, pages 367–381, New York, NY, USA, 2020. Association for Computing Machinery. doi:10.1145/3372885.3373824. | pl |
| dc.description.references | Kazuo Matsuzaka. Sets and Topology (Introduction to Mathematics). IwanamiShoten, 2000. | pl |
| dc.description.references | Keiichi Miyajima and Hiroshi Yamazaki. Compactness of neural networks. Formalized Mathematics, 30(1):13–21, 2022. doi:10.2478/forma-2022-0002. | pl |
| dc.description.references | Tohru Ozawa. Ascoli-Arzel`a theorem. 2012. | pl |
| dc.description.references | Michael Read and Barry Simon. Functional Analysis (Methods of Modern Mathematical Physics). Academic Press, 1980. | pl |
| dc.description.references | Colin Rothgang, Artur Korniłowicz, and Florian Rabe. A new export of the Mizar Mathematical Library. In Fairouz Kamareddine and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics, pages 205–210, Cham, 2021. Springer International Publishing. doi:10.1007/978-3-030-81097-9 17. | pl |
| dc.description.references | Walter Rudin. Functional Analysis. New York, McGraw-Hill, 2nd edition, 1991. | pl |
| dc.description.references | Laurent Schwartz. Th´eorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997. | pl |
| dc.description.references | Laurent Schwartz. Calcul diff´erentiel, tome 2. Analyse. Hermann, 1997. | pl |
| dc.description.references | Hiroshi Yamazaki, Keiichi Miyajima, and Yasunari Shidama. Ascoli-Arzel`a theorem. Formalized Mathematics, 29(2):87–94, 2021. doi:10.2478/forma-2021-0009. | pl |
| dc.description.references | Kosaku Yosida. Functional Analysis. Springer, 1980. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 32 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 141 | pl |
| dc.description.lastpage | 147 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2024, Volume 32, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| AscoliArzel-Theorem-Metric-Space-Version.pdf | 263,76 kB | Adobe PDF | Otwórz |
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