Non-smooth points set of fibres of a semialgebraic mapping. (English) Zbl 1166.57017

Koike, Satoshi; Shiota, Masahiro

J. Math. Soc. Japan 59, No. 4, 953-969 (2007).

The authors consider semialgebraic mappings between semialgebraic sets and define a singular set of points at which the fiber is not smooth. They obtain several interesting properties of the singular set. The main result of the paper states that the singular set is semialgebraic and under some mild conditions it is of codimension at least two. The paper is pleasant to read and contains good illustrative examples.

Reviewer: Zbigniew Hajto (Kraków)

MSC:

57R45	Singularities of differentiable mappings in differential topology
14P10	Semialgebraic sets and related spaces
14P20	Nash functions and manifolds

Keywords:

semialgebraic set; semialgebraic mapping; Nash manifold; semialgebraic triviality