Skip to main content
SpringerLink
Log in

Boolean Algebras

Reihe: Reelle Funktionen (First Edition)

  • Book
  • © 1960

Overview

Authors:
  1. Roman Sikorski

    1. Warsaw-New Orleans-Princeton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 25)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (3 chapters)

  1. Front Matter

    Pages II-IX
    Download chapter PDF

  2. Terminology and notation

    • Roman Sikorski
    Pages 1-1

  3. Finite joins and meets

    • Roman Sikorski
    Pages 2-49

  4. Infinite joins and meets

    • Roman Sikorski
    Pages 50-139

  5. Back Matter

    Pages 139-176
    Download chapter PDF
Back to top

Keywords

About this book

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 proofs. On the contrary, no complete proofs are given in the Appendix which contains mainly a short exposition of applications of Boolean algebras to other parts of Mathematics with references to the literature. An elementary knowledge of discussed theories is supposed.

Authors and Affiliations

  • Warsaw-New Orleans-Princeton, USA

    Roman Sikorski

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation