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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On intrinsic isometries to Euclidean space


Author: A. Petrunin
Translated by: the author
Original publication: Algebra i Analiz, tom 22 (2010), nomer 5.
Journal: St. Petersburg Math. J. 22 (2011), 803-812
MSC (2010): Primary 53C23
Published electronically: June 28, 2011
MathSciNet review: 2828830
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Abstract: Compact metric spaces that admit intrinsic isometries to the Euclidean $ d$-space are considered. Roughly, the main result states that the class of such spaces coincides with the class of inverse limits of Euclidean $ d$-polyhedra.


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Additional Information

A. Petrunin
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email: petrunin@math.psu.edu

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01169-0
PII: S 1061-0022(2011)01169-0
Keywords: Intrinsic isometry, path isometry, Riemannian metric, polyhedron, pro-Euclidean space
Received by editor(s): February 10, 2010
Published electronically: June 28, 2011
Article copyright: © Copyright 2011 American Mathematical Society