analytic set


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analytic set

[‚an·ə¦lid·ik ′set]
(mathematics)
A subset of a separable, complete metric space that is a continuous image of a Borel set in this metric space.
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As a consequence, since any uncountable Borel (or even analytic) set contains a perfect set, the intersection of a Bernstein set with any uncountable analytic set has cardinality c.
He provides all the necessary prerequisites for graduate students and practitioners, describing Riemann surfaces (including coverings, analytical continuation, and Puiseaux expansion), holomorphic functions of several variables (including analytic sets and analytic set germs as well as regular and singular points of analytic sets), isolated singularities of holomorphic functions (including isolated critical points and the universal unfolding), fundamentals of differential topology (including singular homology groups and linking numbers), and the topology of singularities (including the Picard-Lefschetz theorem, the Milnor fibration, the Coxeter-Dynkin diagram, the Selfert form and the action of the braid group.
b) Every compact semialgebraic subset of [omega] which is a global analytic set is also a global Nash set.
If [H.sup.2]([Omega], Z) = 0 and [Mathematical Expression Omitted] is a privileged Bergman submodule of [Mathematical Expression Omitted], then there exists a unique pivileged Bergman submodule S which is isomorphic with [Mathematical Expression Omitted] and so that [S.sup.[perpendicular]] is supported by an analytic set of codimension at least 2 in [Omega].
Our first purpose in this paper is to prove a local holomorphic extension of proper holomorphic mappings under the assumption that the graph of the mapping extends as an analytic set (see Definition 1).
Complex Analytic Sets. Dordrecht: Kluwer Academic Publisher 1989.