| eBook ISBN: | 978-0-8218-9459-0 |
| Product Code: | MEMO/221/1038.E |
| List Price: | $62.00 |
| MAA Member Price: | $55.80 |
| AMS Member Price: | $37.20 |
| eBook ISBN: | 978-0-8218-9459-0 |
| Product Code: | MEMO/221/1038.E |
| List Price: | $62.00 |
| MAA Member Price: | $55.80 |
| AMS Member Price: | $37.20 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 221; 2013; 83 ppMSC: Primary 03; Secondary 54; 28; 26
Let \(\bf\Gamma\) be a Borel class, or a Wadge class of Borel sets, and \(2\!\leq\! d\!\leq\!\omega\) be a cardinal. A Borel subset \(B\) of \({\mathbb R}^d\) is potentially in \(\bf\Gamma\) if there is a finer Polish topology on \(\mathbb R\) such that \(B\) is in \(\bf\Gamma\) when \({\mathbb R}^d\) is equipped with the new product topology. The author provides a way to recognize the sets potentially in \(\bf\Gamma\) and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.
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Table of Contents
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Chapters
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1. Introduction
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2. A condition ensuring the existence of complicated sets
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3. The proof of Theorem 1.10 for the Borel classes
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4. The proof of Theorem 1.11 for the Borel classes
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5. The proof of Theorem 1.10
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6. The proof of Theorem 1.11
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7. Injectivity complements
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Let \(\bf\Gamma\) be a Borel class, or a Wadge class of Borel sets, and \(2\!\leq\! d\!\leq\!\omega\) be a cardinal. A Borel subset \(B\) of \({\mathbb R}^d\) is potentially in \(\bf\Gamma\) if there is a finer Polish topology on \(\mathbb R\) such that \(B\) is in \(\bf\Gamma\) when \({\mathbb R}^d\) is equipped with the new product topology. The author provides a way to recognize the sets potentially in \(\bf\Gamma\) and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.
-
Chapters
-
1. Introduction
-
2. A condition ensuring the existence of complicated sets
-
3. The proof of Theorem 1.10 for the Borel classes
-
4. The proof of Theorem 1.11 for the Borel classes
-
5. The proof of Theorem 1.10
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6. The proof of Theorem 1.11
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7. Injectivity complements
