A Course on Borel SetsSpringer Science & Business Media, 13.04.1998 - 264 Seiten A 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. |
Inhalt
Cardinal and Ordinal Numbers | 1 |
Topological Preliminaries | 39 |
Standard Borel Spaces | 80 |
Analytic and Coanalytic Sets | 127 |
The First Separation Theorem | 147 |
Reduction Theorems | 171 |
1 | 184 |
242 | |
Glossary | 250 |
261 | |
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Häufige Begriffe und Wortgruppen
A-measurable admits a Borel algebra analytic sets analytic subsets assume Baire Baire category theorem Baire property bijection Borel function Borel isomorphism Borel map Borel measurable Borel set Borel subset called Cantor cardinality cl(U Clearly closed set closed subset closed under countable coanalytic comeager completely metrizable continuous map contradiction convergent Corollary countable base countable intersections countable unions defined denote dense element equivalence classes Example Exercise finite function f Gs set Hence homeomorphic induction infinite integer irr(A irr(n Let f Let G lim sup map ƒ meager measurable space nonempty open set nonmeager Note o-algebra one-to-one open set ordinal numbers pairwise disjoint partition pointclass Polish group Polish space Polish topology Proposition prove real numbers result follows second countable separable sequence Souslin operation Suppose Take topological space uncountable Polish space w₁ well-ordered set zero-dimensional Zorn's lemma
Beliebte Passagen
Seite 244 - Kechris and A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser., 128, Cambridge Univ.