On the topology of semi-algebraic functions on closed semi-algebraic sets
نویسندگان
چکیده
منابع مشابه
On the topology of semi-algebraic functions on closed semi-algebraic sets
We consider a closed semi-algebraic set X ⊂ R and a C semi-algebraic function f : R → R such that f|X has a finite number of critical points. We relate the topology of X to the topology of the sets {f ∗ α}, where ∗ ∈ {≤,=,≥} and α ∈ R, and the indices of the critical points of f|X and −f|X . We also relate the topology of X to the topology of the links at infinity of the sets {f ∗ α} and the in...
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ژورنال
عنوان ژورنال: Manuscripta Mathematica
سال: 2012
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-011-0523-0