This thesis analyses the semialgebraic sets, that is, a finite union of solu- tions to a finite sequence of polynomial inequalities. We introduce a notion of cylindrical algebraic decomposition as a tool for the construction of a semialge- braic stratification and a triangulation of a semialgebraic set. On this basis, we prove several important and well-known results of real algebraic geometry, such as Hardt's semialgebraic triviality or Sard's theorem. Drawing on Morse theory, we finally give a proof of a Thom-Milnor bound for a sum of Betti numbers of a real algebraic set. 1
Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:357111 |
Date | January 2017 |
Creators | Raclavský, Marek |
Contributors | Šťovíček, Jan, Příhoda, Pavel |
Source Sets | Czech ETDs |
Language | Czech |
Detected Language | English |
Type | info:eu-repo/semantics/masterThesis |
Rights | info:eu-repo/semantics/restrictedAccess |
Page generated in 0.0017 seconds