In mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation was for the proof of Deligne's conjecture on Hochschild cohomology. Robert Hardt, Pascal Lambrechts, Victor Turchin, and Ismar Volić later developed the theory.
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In mathematics, a piecewisealgebraicspace is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation...
functions piecewise linear functions continuous functions, compact open topology all functions, space of pointwise convergence Hardy space Hölder space Càdlàg...
the compact metric space B 2 d g ( p , q ) ( p ) ¯ , {\displaystyle {\overline {B_{2d_{g}(p,q)}(p)}},} to a sequence of piecewise continuously differentiable...
In mathematics, a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure...
\,.} For some scalar field f : U ⊆ R2 → R, the line integral along a piecewise smooth curve C ⊂ U is defined as ∫ C f d s = ∫ a b f ( r ( t ) ) | r ′...
inside an algebraic subvariety of the same dimension. Łojasiewicz inequality Existential theory of the reals Subanalytic set piecewisealgebraicspace Bochnak...
piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear...
This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...
Euclidean space, an algebraic variety is glued together from affine algebraic varieties, which are zero sets of polynomials over algebraically closed fields...
Alexander also proved that the theorem does hold in three dimensions for piecewise linear/smooth embeddings. This is one of the earliest examples where the...
mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with...
{ x ∈ R : x ≠ 0 } {\displaystyle \{x\in \mathbb {R} :x\neq 0\}} . The piecewise function f {\displaystyle f} defined by f ( x ) = { 1 / x x ≠ 0 0 x =...
of algebraic surfaces and algebraic varieties defined on number fields and their field extensions. Connes embedding problem in Von Neumann algebra theory...
value only for algebraic objects for which the notion of an absolute value is defined, notably an element of a normed division algebra, for example a...
In abstract algebra, a semiring is an algebraic structure. It is a generalization of a ring, dropping the requirement that each element must have an additive...
function must pass through the origin. Homogeneous function Nonlinear system Piecewise linear function Linear approximation Linear interpolation Discontinuous...
to the spectral method). However, we take V {\displaystyle V} as a space of piecewise polynomial functions for the finite element method. We take the interval...
smooth functions between differentiable manifolds, PL for piecewise linear functions between piecewise linear manifolds, and TOP for continuous functions between...
and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra...
m-dimensional Euclidean space, if m is large enough (depending on n), the sphere should be unknotted. In general, piecewise-linear n-spheres form knots...
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