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Proceedings of the American Mathematical Society

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

 

 

Regular neighborhoods and topological manifolds


Author: Glenn P. Weller
Journal: Proc. Amer. Math. Soc. 42 (1974), 320-325
MSC: Primary 57A40
DOI: https://doi.org/10.1090/S0002-9939-1974-0328949-3
MathSciNet review: 0328949
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Abstract: This paper defines a notion of topological regular neighborhood for compact triangulable subspaces of topological manifolds, proves a uniqueness theorem for such neighborhoods, and shows that this theorem is in a sense the best possible. These results have obvious applications to regular neighborhoods in manifolds having more than one piecewise linear structure.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0328949-3
Keywords: Topological manifold, piecewise linear manifold, regular neighborhood, triangulation, Hauptvermutung, Whitehead torsion, mapping cylinder neighborhood, open cone neighborhood
Article copyright: © Copyright 1974 American Mathematical Society