Neighborhoods of algebraic sets

Durfee, Alan H.

doi:10.1090/S0002-9947-1983-0688959-3

Neighborhoods of algebraic sets
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Trans. Amer. Math. Soc. 276 (1983), 517-530 Request permission

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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