Slicing theorems for spheres in Euclidean space
Author:
Robert J. Daverman
Journal:
Trans. Amer. Math. Soc. 166 (1972), 479489
MSC:
Primary 57A35
MathSciNet review:
0295356
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Abstract: This paper describes conditions on the intersection of an nsphere in Euclidean space with the horizontal hyperplanes of sufficient to determine that the sphere be nicely embedded. The results generally are pointed towards showing that the complement of is 1ULC (uniformly locally 1connected) rather than towards establishing the stronger property that is locally flat. For instance, the main theorem indicates that is 1ULC provided each nondegenerate intersection of and a horizontal hyperplane be an sphere bicollared both in that hyperplane and in itself .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197202953564
PII:
S 00029947(1972)02953564
Keywords:
Horizontal hyperplane of Euclidean space,
bicollared submanifold,
locally flat submanifold,
locally simply connected,
homeomorphic approximation,
topological embedding
Article copyright:
© Copyright 1972
American Mathematical Society
