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- Title
Separating families for semi-algebraic sets.
- Authors
Marshall, Murray
- Abstract
A new invariant p( V) is defined for real algebraic varieties V which measures the complexity of semi-algebraic sets in V. p( V) is the least integer such that every semi-algebraic set S ⊂- V can be separated from its compliment by p( V) polynomials. This is a very natural invariant to consider. Using results of Bröcker [4-8] and generalizations of Bröcker's results found in [16,17], upper bounds for p( V) are computed. The proof is simpler than the proof of similar results in [5-9],[15-18] since the complicated local-global formula for the stability index and the various pasting techniques are not needed. Lower bounds for p( V) are also computed in some special cases, the technique here being to first study the corresponding invariant p( X, G) for a finite space of orderings ( X, G) [13,14].
- Publication
Manuscripta Mathematica, 1993, Vol 80, Issue 1, p73
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF03026537