Functional Space Consisted by Continuous Functions on Topological Space

Pole DC	Wartość	Język
dc.contributor.author	Yamazaki, Hiroshi	-
dc.contributor.author	Miyajima, Keiichi	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2021-08-30T09:06:00Z	-
dc.date.available	2021-08-30T09:06:00Z	-
dc.date.issued	2021	-
dc.identifier.citation	Formalized Mathematics, Volume 29, Issue 1, Pages 49-62	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/11411	-
dc.description.abstract	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.	pl
dc.language.iso	en	pl
dc.publisher	DeGruyter Open	pl
dc.rights	Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)	-
dc.rights.uri	https://creativecommons.org/licenses/by-sa/3.0/	-
dc.subject	continuous function space	pl
dc.subject	compact topological space	pl
dc.subject	Banach space	pl
dc.title	Functional Space Consisted by Continuous Functions on Topological Space	pl
dc.type	Article	pl
dc.rights.holder	© 2021 University of Białymstoku	pl
dc.rights.holder	CC-BY-SA License ver. 3.0 or later	pl
dc.identifier.doi	10.2478/forma-2021-0005	-
dc.description.Affiliation	Hiroshi Yamazaki - Nagano Prefectural Institute of Technology, Nagano, Japan	pl
dc.description.Affiliation	Keiichi Miyajima - Ibaraki University, Ibaraki, Japan	pl
dc.description.Affiliation	Yasunari Shidama - Karuizawa Hotch 244-1, Nagano, Japan	pl
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3- 319-20614-1. doi:10.1007/978-3-319-20615-8 17.	pl
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	pl
dc.description.references	Bruce K. Driver. Analysis Tools with Applications. Springer, Berlin, 2003.	pl
dc.description.references	Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269–275, 2004.	pl
dc.description.references	Laurent Schwartz. Théorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997.	pl
dc.description.references	Yasumasa Suzuki. Banach space of bounded real sequences. Formalized Mathematics, 12 (2):77–83, 2004.	pl
dc.description.references	Hiroshi Yamazaki. Functional sequence in norm space. Formalized Mathematics, 28(4): 263–268, 2020. doi:10.2478/forma-2020-0023.	pl
dc.identifier.eissn	1898-9934	-
dc.description.volume	29	pl
dc.description.issue	1	pl
dc.description.firstpage	49	pl
dc.description.lastpage	62	pl
dc.identifier.citation2	Formalized Mathematics	pl
Występuje w kolekcji(ach):	Formalized Mathematics, 2021, Volume 29, Issue 1

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