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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$ C^k$-quasi-isometry sets are pre-compact


Authors: F. T. Farrell and P. Ontaneda
Journal: Proc. Amer. Math. Soc. 138 (2010), 737-741
MSC (2000): Primary 58A05, 58D05, 58D17, 58D19
Published electronically: October 9, 2009
MathSciNet review: 2557190
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a closed smooth manifold. By an argument formally similar to one used in constructing the Levi-Civita connection, it is shown that $ C^k$-quasi-isometry sets in $ DIFF^{k+1}(M)$ are $ C^{k+1}$-bounded, where $ 0\leq k< \infty$. This implies, using the Arsela-Ascoli theorem, that such sets are pre-compact in $ DIFF^{k}(M)$.


References [Enhancements On Off] (What's this?)

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Additional Information

F. T. Farrell
Affiliation: Department of Mathematics, State University of New York, Binghamton, New York 13902

P. Ontaneda
Affiliation: Department of Mathematics, State University of New York, Binghamton, New York 13902

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10132-6
PII: S 0002-9939(09)10132-6
Received by editor(s): March 4, 2009
Received by editor(s) in revised form: March 6, 2009
Published electronically: October 9, 2009
Additional Notes: Both authors were partially supported by NSF grants.
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2009 American Mathematical Society