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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Largest normal neighborhoods


Author: V. Ozols
Journal: Proc. Amer. Math. Soc. 61 (1976), 99-101
MSC: Primary 57D70; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1976-0431220-4
MathSciNet review: 0431220
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Abstract: It is well known that the largest normal neighborhood of a point in a compact Riemannian manifold is a Euclidean cell, that is, homeomorphic to the open unit ball. In this paper it is proved that this normal neighborhood is in fact $ {C^\infty }$ diffeomorphic to the open unit ball. The method is to paste together a sequence of $ {C^\infty }$ radial dilations which combine to engulf an open ball or all of $ {{\mathbf{R}}^n}$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0431220-4
Keywords: Cut locus, normal neighborhood, engulfing
Article copyright: © Copyright 1976 American Mathematical Society