Axiom of choice (eBook, 2006) []
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Axiom of choice

Author: Horst Herrlich
Publisher: Berlin : Springer, ©2006.
Series: Lecture notes in mathematics, 1876.
Edition/Format:   eBook : Document : EnglishView all editions and formats

AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. Illuminating examples are drawn from diverse areas of mathematics, particularly from  Read more...


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Additional Physical Format: Axiom of choice
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Horst Herrlich
ISBN: 9783540342687 3540342680 9783540309895 3540309896
OCLC Number: 314342436
Description: 1 online resource (XIV, 194 p.) : illustrations
Contents: 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).
Series Title: Lecture notes in mathematics, 1876.
Responsibility: Horst Herrlich.


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From the reviews:"The book is an excellent introduction to the Axiom of Choice, its consequences and even its possible replacements. Although the author claims not to have written a textbook, Read more...

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