Scalar curvature of defineable CAT-spaces.
Self-adjoint determinantal representations of real plane curves.
Semialgebraic and semianalytic sets
Semi-algebraic complexity-additive complexity of diagonalization of quadratic forms.
We study matrix calculations such as diagonalization of quadratic forms under the aspect of additive complexity and relate these complexities to the complexity of matrix multiplication. While in Bürgisser et al. (1991) for multiplicative complexity the customary thick path existence argument was sufficient, here for additive complexity we need the more delicate finess of the real spectrum (cf. Bochnak et al. (1987), Becker (1986), Knebusch and Scheiderer (1989)) to obtain a complexity relativization....
Semi-algebraic neighborhoods of closed semi-algebraic sets
Given a closed (not necessarly compact) semi-algebraic set in , we construct a non-negative semi-algebraic function such that and such that for sufficiently small, the inclusion of in is a retraction. As a corollary, we obtain several formulas for the Euler characteristic of .
Semialgebraic Topology Over a Real Closed Field I: Paths and Components in the Set of Rational Points of an Algebraic Variety.
Semialgebraic Topology over a Real Closed Field II: Basic Theory of Semialgebraic Spaces.
Semialgebraicity of certain local loci
Semianalytic and subanalytic sets
Semi-monotone sets
A coordinate cone in is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...
Separably Real Closed Local Rings.
Separating families for semi-algebraic sets.
Separating ideals in dimension 2.
Experience shows that in geometric situations the separating ideal associated with two orderings of a ring measures the degree of tangency of the corresponding ultrafilters of semialgebraic sets. A related notion of separating ideals is introduced for pairs of valuations of a ring. The comparison of both types of separating ideals helps to understand how a point on a surface is approached by different half-branches of curves.
Separation, factorization and finite sheaves on Nash manifolds
Separation of global semianalytic sets
Given global semianalytic sets A and B, we define a minimal analytic set N such that Ā∖N and B̅∖N can be separated by an analytic function. Our statement is very similar to the one proved by Bröcker for semialgebraic sets.
Sets with the Bernstein and generalized Markov properties
It is known that for determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not determining. In this paper we give examples of sets which are not determining, but have the Bernstein and generalized Markov properties.
Sheaves on subanalytic sites
Siciak's extremal function in complex and real analysis
The Siciak extremal function establishes an important link between polynomial approximation in several variables and pluripotential theory. This yields its numerous applications in complex and real analysis. Some of them can be found on a rich list drawn up by Klimek in his well-known monograph "Pluripotential Theory". The purpose of this paper is to supplement it by applications in constructive function theory.
Signatures and flatness.
Signatures et composantes connexes.