Global almost analytic algebraicity of analytic sets

Wojciech Kucharz

Vol. 143 (1990), No. 2, 287–300

DOI: 10.2140/pjm.1990.143.287

Abstract

Let X be a nonsingular real algebraic subset of Rⁿ. There are known several results concerning analytic subsets of X which are analytically or C^r equivalent to algebraic sets, i.e., which can be transformed by an analytic or C^r diffeomorphism, r = 0,1,2,… , of X onto algebraic subsets. In general, C^r equivalence does not imply analytic equivalence. However, we show in this paper that C^r equivalence often can be replaced by, much stronger, “almost analytic” equivalence.

Mathematical Subject Classification 2000

Primary: 14P15

Secondary: 32C05, 57R95, 58A07

Milestones

Received: 3 February 1987

Revised: 27 July 1989

Published: 1 June 1990