# Mazur-Ulam Theorem

Formalized Mathematics (2011)

- Volume: 19, Issue: 3, page 127-130
- ISSN: 1426-2630

## Access Full Article

top## Abstract

top## How to cite

topArtur Korniłowicz. "Mazur-Ulam Theorem." Formalized Mathematics 19.3 (2011): 127-130. <http://eudml.org/doc/267439>.

@article{ArturKorniłowicz2011,

abstract = {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.},

author = {Artur Korniłowicz},

journal = {Formalized Mathematics},

language = {eng},

number = {3},

pages = {127-130},

title = {Mazur-Ulam Theorem},

url = {http://eudml.org/doc/267439},

volume = {19},

year = {2011},

}

TY - JOUR

AU - Artur Korniłowicz

TI - Mazur-Ulam Theorem

JO - Formalized Mathematics

PY - 2011

VL - 19

IS - 3

SP - 127

EP - 130

AB - 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.

LA - eng

UR - http://eudml.org/doc/267439

ER -

## References

top- 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. Zbl58.0423.01
- 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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.