A Course on Borel SetsA Course on Borel sets provides a thorough introduction to Borel sets and measurable selections and acts as a stepping stone to descriptive set theory by presenting important techniques such as universal sets, prewellordering, scales, etc. It is well suited for graduate students exploring areas of mathematics for their research and for mathematicians requiring Borel sets and measurable selections in their work. It contains significant applications to other branches of mathematics and can serve as a self- contained reference accessible by mathematicians in many different disciplines. It is written in an easily understandable style and employs only naive set theory, general topology, analysis, and algebra. A large number of interesting exercises are given throughout the text. |
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Sommario
Cardinal and Ordinal Numbers | 1 |
Topological Preliminaries | 39 |
Standard Borel Spaces 81 | 80 |
Analytic and Coanalytic Sets | 127 |
Selection and Uniformization Theorems | 183 |
| 241 | |
| 250 | |
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algebra analytic sets analytic subsets applications assume Baire Borel isomorphism Borel map Borel set Borel subset called Cantor cardinality chapter Choose claim Clearly closed set coanalytic comeager compact completely metrizable Consider containing contradiction convergent Corollary countable cross section define defined denote dense easy element equivalence relation Example Exercise exists extends finite first follows function Further give Hence holds homeomorphic induction intersections lemma Let X meager measurable measurable space metric metrizable space nonempty Note numbers one-to-one open set operation pairwise disjoint particular partition Polish space projection Proof Proposition prove range Remark result result follows satisfying second countable selection separable sequence Suppose Take Theorem theory topology tree true uncountable uniformization universal well-ordered set write
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Pagina 244 - Kechris and A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser., 128, Cambridge Univ.
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Informazioni bibliografiche
| Titolo | A Course on Borel Sets Volume 180 di Graduate Texts in Mathematics |
| Autore | S.M. Srivastava |
| Edizione | illustrata |
| Editore | Springer Science & Business Media, 1998 |
| ISBN | 0387984127, 9780387984124 |
| Lunghezza | 264 pagine |
| Esporta citazione | BiBTeX EndNote RefMan |