# semialgebraic

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**Semialgebraic set**— In mathematics, a semialgebraic set is a subset S of real n dimensional space defined by a finite sequence of polynomial equations and inequalities; or any finite union of such sets. Such sets are studied as an extension of real algebraic… … Wikipedia**Semialgebraic space**— In mathematics, especially in real algebraic geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set.DefinitionLet U be an open subset of R n for some n . A semialgebraic function on U is defined to be a… … Wikipedia**Mnev's universality theorem**— In algebraic geometry, Mnev s universality theorem is a result which can be used to represent algebraic (or semi algebraic) varieties as realizations of oriented matroids, a notion of combinatorics. Contents 1 Oriented matroids 2 Stable… … Wikipedia**Nash functions**— In real algebraic geometry, a Nash function on an open semialgebraic subset U ⊂ Rn is an analytic function f: U → R satisfying a non trivial polynomial equation P(x,f(x)) = 0 for all x in U (A semialgebraic subset of Rn is a subset obtained from… … Wikipedia**Tarski–Seidenberg theorem**— In mathematics, the Tarski–Seidenberg theorem states that a set in n +1 dimensional space defined by polynomial identities and inequalities can be projected down onto n dimensional space, and the resulting set is still definable in terms of… … Wikipedia**Sheaf (mathematics)**— This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… … Wikipedia**Stengle's Positivstellensatz**— In mathematics, Stengle s Positivstellensatz characterizes polynomials which are positive on a given semialgebraic set over the real numbers, or more generally, any real closed field. It can be thought of as an ordered analogue of Hilbert s… … Wikipedia**List of mathematics articles (S)**— NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… … Wikipedia**O-minimal theory**— In mathematical logic, and more specifically in model theory, a totally ordered structure ( M , lt;,...) is o minimal if and only if every definable set X sub; M (with parameters) can be realized as a finite union of intervals and points.A theory … Wikipedia**o-minimal theory**— In mathematical logic, and more specifically in model theory, an infinite structure (M,<,...) which is totally ordered by < is called an o minimal structure if and only if every definable subset X ⊂ M (with parameters taken from… … Wikipedia