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Displaying similar documents to “Some approximation problems in semi-algebraic geometry”

Additive generators of discrete semi-uninorms

Ya-Ming Wang, Hang Zhan, Yuan-Yuan Zhao (2024)

Kybernetika

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This work explores commutative semi-uninorms on finite chains by means of strictly increasing unary functions and the usual addition. In this paper, there are three families of additively generated commutative semi-uninorms. We not only study the structures and properties of semi-uninorms in each family but also show the relationship among these three families. In addition, this work provides the characterizations of uninorms in 𝒰 min and 𝒰 max that are generated by additive generators. ...

On homotopy types of limits of semi-algebraic sets and additive complexity of polynomials

Sal Barone, Saugata Basu (2014)

Journal of the European Mathematical Society

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We prove that the number of distinct homotopy types of limits of one-parameter semi-algebraic families of closed and bounded semi-algebraic sets is bounded singly exponentially in the additive complexity of any quantifier-free first order formula defining the family. As an important consequence, we derive that the number of distinct homotopy types of semi-algebraic subsets of ℝ k defined by a quantifier-free first order formula Φ , where the sum of the additive complexities of the polynomials...

Local approximation of semialgebraic sets

Massimo Ferrarotti, Elisabetta Fortuna, Les Wilson (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let A be a closed semialgebraic subset of euclidean space of codimension at least one, and containing the origin O as a non-isolated point. We prove that, for every real s ≥ 1 , there exists an algebraic set V which approximates A to order s at O . The special case s = 1 generalizes the result of the authors that every semialgebraic cone of codimension at least one is the tangent cone of an algebraic set.

Cycles on algebraic models of smooth manifolds

Wojciech Kucharz (2009)

Journal of the European Mathematical Society

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Every compact smooth manifold M is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of M . We study modulo 2 homology classes represented by algebraic subsets of X , as X runs through the class of all algebraic models of M . Our main result concerns the case where M is a spin manifold.

Property of being semi-Kelley for the cartesian products and hyperspaces

Enrique Castañeda-Alvarado, Ivon Vidal-Escobar (2017)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we construct a Kelley continuum X such that X × [ 0 , 1 ] is not semi-Kelley, this answers a question posed by J.J. Charatonik and W.J. Charatonik in A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69–99. In addition, we show that the hyperspace C ( X ) is not semi- Kelley. Further we show that small Whitney levels in C ( X ) are not semi-Kelley, answering a question posed by A. Illanes in Problemas propuestos para el taller de Teoría de continuos y sus hiperespacios, Queretaro,...

On the space of morphisms into generic real algebraic varieties

Riccardo Ghiloni (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let Z be a real algebraic variety. We say that Z is generic if there exist a finite family { D i } i = 1 n of irreducible real algebraic curves with genus ≥ 2 and a biregular embedding of Z into the product variety ∏ i = 1 n D i . A bijective map ϕ : Z ˜ 1 → Z from a real algebraic variety Z ˜ to Z is called weak change of the algebraic structure of  Z if it is regular and its inverse is a Nash map. Generic real algebraic...