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Titlebook: Boolean Algebras; Reihe: Reelle Funkti Roman Sikorski Book 19601st edition Springer-Verlag Berlin Heidelberg 1960 Boolescher Verband.Finite

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期刊全称Boolean Algebras
期刊简称Reihe: Reelle Funkti
影响因子2023Roman Sikorski
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学科分类Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
图书封面Titlebook: Boolean Algebras; Reihe: Reelle Funkti Roman Sikorski Book 19601st edition Springer-Verlag Berlin Heidelberg 1960 Boolescher Verband.Finite
影响因子There are two aspects in the theory of Boolean algebras: algebraic and set-theoretical. Boolean algebras can be considered as a special kind of algebraic rings, or as a generalization of the set-theoretical notion of field of sets. Fundamental theorems in the both directions are due to M. H. STONE whose papers have opened a new period in the development of the theory. This work treats of the set-theoretical aspect, the algebraic one being scarcely mentioned. The book is composed of two Chapters and an Appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only. A greater part of its contents can be found also in the books of BIRKHOFF [2J and HERMES [1 J. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters land II it suffices to know only fundamental notions from General Set Theory and Set-theoretical Topology. No knowledge of Lattice Theory or AbstractAlgebra is supposed. Less known topological theorems are recalled. Only a few examples use more advanced topological means but they can be omitted. All theorems in both Chapters are given with full pr
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Infinite joins and meets,Let A., . . . ,.. be elements of a Boolean algebra A. The finite join .is the least element containing all elements .., . . . ,.. i. e. it is characterized uniquely by the following two conditions:
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https://doi.org/10.1007/b119172 properties as the set-theoretical union, intersection and complementation of subsets of a fixed space. Since the elements of A have many properties of sets, we shall denote them by capital letters .,... used generally to denote sets. For arbitrary elements . ∈ A, . ∪ . and . ∩ . are elements in A,
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Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folgehttp://image.papertrans.cn/b/image/189772.jpg
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https://doi.org/10.1007/978-3-662-01492-9Boolescher Verband; Finite; Mathematica; Morphism; algebra; calculus; function; logic; mathematics; proof; set
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Book 19601st editionons from General Set Theory and Set-theoretical Topology. No knowledge of Lattice Theory or AbstractAlgebra is supposed. Less known topological theorems are recalled. Only a few examples use more advanced topological means but they can be omitted. All theorems in both Chapters are given with full pr
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