Topological open problems in the geometry of Banach spaces.
J. Orihuela (2007)
Extracta Mathematicae
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J. Orihuela (2007)
Extracta Mathematicae
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Petr Hájek, Michal Johanis (2003)
Open Mathematics
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In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains...
Hideki Sakurai, Hisayoshi Kunimune, Yasunari Shidama (2008)
Formalized Mathematics
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In this article we formalize one of the most important theorems of linear operator theory the Open Mapping Theorem commonly used in a standard book such as [8] in chapter 2.4.2. It states that a surjective continuous linear operator between Banach spaces is an open map.MML identifier: LOPBAN 6, version: 7.10.01 4.111.1036
Zarghami, R. (2010)
The Journal of Nonlinear Sciences and its Applications
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Gozali, S.M., Gunawan, H., Neswan, O. (2010)
Annals of Functional Analysis (AFA) [electronic only]
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Chmieliński, Jacek (2007)
Banach Journal of Mathematical Analysis [electronic only]
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Mazaheri, H., Kazemi, R. (2007)
Novi Sad Journal of Mathematics
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J. Talponen (2007)
Extracta Mathematicae
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Heath, Matthew J. (2009)
Banach Journal of Mathematical Analysis [electronic only]
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Rincon, A., Liu, I-Shih (2003)
Divulgaciones Matemáticas
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Plichko, Anatolij (1997)
Serdica Mathematical Journal
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* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95. The main results of the paper are: Theorem 1. Let a Banach space E be decomposed into a direct sum of separable and reflexive subspaces. Then for every Hausdorff locally convex topological vector space Z and for every linear continuous bijective operator T : E → Z, the inverse T^(−1) is a Borel map. Theorem 2. Let us assume the continuum hypothesis....