Some analytic bounds for subanalytic sets. (English) Zbl 0547.32003

Differential geometric control theory, Proc. Conf., Mich. Technol. Univ. 1982, Prog. Math. 27, 259-267 (1983).
[For the entire collection see Zbl 0503.00014.]
This conference lecture collects several results which say that various numerical data associated with subanalytic maps are bounded provided the domain is compact. These data include the distance of image points, the Hausdorff measure of the fibres, the number of simplices needed in a triangulation of the fibre. The indicated proofs rely heavily on earlier results of the author, in particular on his paper in Am. J. Math. 102, 291-302 (1980; Zbl 0465.14012).
Reviewer: K.Lamotke


32B20 Semi-analytic sets, subanalytic sets, and generalizations
32B25 Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions