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http://hdl.handle.net/11320/3720
Tytuł: | Topological Properties of Real Normed Space |
Autorzy: | Nakasho, Kazuhisa Futa, Yuichi Shidama, Yasunari |
Słowa kluczowe: | functional analysis normed linear space topological vector space |
Data wydania: | 2014 |
Data dodania: | 9-gru-2015 |
Wydawca: | De Gruyter Open |
Źródło: | Formalized Mathematics, Volume 22, Issue 3, 2014, Pages 209-223 |
Abstrakt: | In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences is also refered here. Then we argue the condition when real normed subspaces become Banach’s spaces. We also formalize quotient vector space. In the last session, we argue the properties of the closure of real normed space. These formalizations are based on [19](p.3-41), [2] and [34](p.3-67). |
Afiliacja: | Nakasho Kazuhisa - Shinshu University Nagano, Japan Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, Japan Shidama Yasunari - Shinshu University Nagano, Japan |
URI: | http://hdl.handle.net/11320/3720 |
DOI: | 10.2478/forma-2014-0024 |
ISSN: | 1426-2630 1898-9934 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2014, Volume 22, Issue 3 |
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