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2011 | 19 | 3 | 127-130
Tytuł artykułu

Mazur-Ulam Theorem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Mazur-Ulam theorem [15] has been formulated as two registrations: cluster bijective isometric -> midpoints-preserving Function of E, F; and cluster isometric midpoints-preserving -> Affine Function of E, F; A proof given by Jussi Väisälä [23] has been formalized.
Słowa kluczowe
Wydawca
Rocznik
Tom
19
Numer
3
Strony
127-130
Opis fizyczny
Daty
wydano
2011-01-01
online
2012-04-26
Twórcy
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland
Bibliografia
  • Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.
  • Józef Białas and Yatsuka Nakamura. Dyadic numbers and T4 topological spaces. Formalized Mathematics, 5(3):361-366, 1996.
  • Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • Agata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990.
  • Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.
  • Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
  • Artur Korniłowicz. Collective operations on number-membered sets. Formalized Mathematics, 17(2):99-115, 2009, doi: 10.2478/v10037-009-0011-0.[Crossref]
  • Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.
  • Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
  • Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
  • Stanisław Mazur and Stanisław Ulam. Sur les transformationes isométriques d'espaces vectoriels normés. C. R. Acad. Sci. Paris, (194):946-948, 1932.
  • Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.
  • Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  • Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • Jussi Väisälä. A proof of the Mazur-Ulam theorem.
  • Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-011-0020-7
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