Mazur-Ulam Theorem

Artur Korniłowicz

Formalized Mathematics (2011)

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

Abstract

top
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.

How to cite

top

Artur 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
  1. Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991. 
  3. Józef Białas and Yatsuka Nakamura. Dyadic numbers and T4 topological spaces. Formalized Mathematics, 5(3):361-366, 1996. 
  4. Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  5. Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  6. Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  7. Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  8. Agata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990. 
  9. Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991. 
  10. Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004. 
  11. Artur Korniłowicz. Collective operations on number-membered sets. Formalized Mathematics, 17(2):99-115, 2009, doi: 10.2478/v10037-009-0011-0.[Crossref] 
  12. Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990. 
  13. Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  14. Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. 
  15. 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
  16. Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  17. Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. 
  18. Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  19. Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991. 
  20. Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003. 
  21. Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  22. Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  23. Jussi Väisälä. A proof of the Mazur-Ulam theorem. 
  24. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  25. Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.