In mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Kontsevich and Soibelman. The motivation was for the proof of Deligne's conjecture on Hochschild cohomology. Hardt, Lambrechts, Turchin, and Volić later developed the theory. References Maxim Kontsevich and Yan Soibelman. “Deformations of algebras over operads and the Deligne conjecture”. In: Conférence Moshé Flato 1999, Vol. I (Dijon). Vol. 21. Math. Phys. Stud. Dordrecht: Kluwer Acad. Publ., 2000, pp. 255–307. arXiv: math/0001151. Algebraic geometry