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Journal Article
Largest Normal Neighborhoods
V. Ozols
Proceedings of the American Mathematical Society
Vol. 61, No. 1 (Nov., 1976), pp. 99-101
Published
by: American Mathematical Society
DOI: 10.2307/2041672
https://www.jstor.org/stable/2041672
Page Count: 3
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Topics: Riemann manifold, Continuous functions, Coordinate systems, Unit ball, Mathematical theorems
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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 $\mathbf{R}^n$.
Proceedings of the American Mathematical Society
© 1976 American Mathematical Society