REFLECTIONS AND A GENERALIZATION OF THE MAZUR-ULAM THEOREM

In this paper, we will generalize the Mazur-Ulam theorem which states that every bijective isometry between two normed spaces is affine. To do this, we introduce a notion of metricoid spaces, which is a generalization of metric space. Finally, we give a representation of surjections from C⁺(X) onto...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2012-01, Vol.42 (1), p.117-150
Main Authors: HATORI, OSAMU, KOBAYASHI, KIYOTAKA, MIURA, TAKESHI, TAKAHASI, SIN-EI
Format: Article
Language:English
Subjects:
46B04
46J10
Algebra
Applied mathematics
Hausdorff spaces
Homeomorphism
Integers
isometries
Mathematical theorems
metricoid groups
metricoid spaces
Natural numbers
Real numbers
the Banach-Stone theorem
The Mazur-Ulam theorem
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Summary:In this paper, we will generalize the Mazur-Ulam theorem which states that every bijective isometry between two normed spaces is affine. To do this, we introduce a notion of metricoid spaces, which is a generalization of metric space. Finally, we give a representation of surjections from C⁺(X) onto C⁺(Y) which preserve certain subdistances.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmj-2012-42-1-117