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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Neighborhoods of algebraic sets


Author: Alan H. Durfee
Journal: Trans. Amer. Math. Soc. 276 (1983), 517-530
MSC: Primary 32B20; Secondary 14G30, 32B25
MathSciNet review: 688959
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Abstract: In differential topology, a smooth submanifold in a manifold has a tubular neighborhood, and in piecewise-linear topology, a subcomplex of a simplicial complex has a regular neighborhood. The purpose of this paper is to develop a similar theory for algebraic and semialgebraic sets. The neighborhoods will be defined as level sets of polynomial or semialgebraic functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0688959-3
PII: S 0002-9947(1983)0688959-3
Keywords: Tubular neighborhood, regular neighborhood, rug function, link of singularity, stratification, Milnor fibration theorem, semialgebraic sets
Article copyright: © Copyright 1983 American Mathematical Society