Axiom of Choice / by Horst Herrlich
(Lecture Notes in Mathematics ; 1876)
| データ種別 | 電子ブック |
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| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg , 2006 |
| 本文言語 | 英語 |
| 大きさ | XIV, 198 p. 1 illus : online resource |
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| 内容注記 | Origins: Hilbert's First Problem Choice Principles: Some Equivalents to the Axiom of Choice, Some Concepts Related to the Axiom of Choice Elementary Observations: Hidden Choice, Unnecessary Choice, Concepts Split Up: Compactness Disasters without Choice: Finiteness, Disasters in Cardinal Arithmetic, Disasters in Order Theory, Disasters in Algebra I: Vector Spaces, Disasters in Algebra II: Categories, Disasters in Elementary Analysis: The Reals and Continuity, Disasters in Topology I: Countable Sums, Disasters in Topology II: Products (The Tychonoff and the Cech-Stone Theorem), Disasters in Topology III: Function Spaces (The Ascoli Theorem), Disasters in Topology IV: The Baire Category Theorem, Disasters in Graph Theory: Coloring Problems Disasters with Choice: Disasters in Elementary Analysis, Disasters in Geometry: Paradoxical Decompositions Disasters either way: Disasters in Game Theory Beauty without Choice: Lindelöf = Compact, Measurability (The Axiom of Determinateness) |
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| 一般注記 | AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that: Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC). Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games). Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness). Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory |
| 著者標目 | *Herrlich, Horst author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebra LCSH:Functional analysis LCSH:Game theory LCSH:Mathematical logic LCSH:Topology LCSH:Combinatorics FREE:Mathematics FREE:Mathematical Logic and Foundations FREE:General Algebraic Systems FREE:Functional Analysis FREE:Game Theory, Economics, Social and Behav. Sciences FREE:Combinatorics FREE:Topology |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9783540342687 
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| ISBN | 9783540342687 |
| URL | http://dx.doi.org/10.1007/11601562 |
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