_:N41dafad172c54f7989a9c4f205b99ce0 .
"set-theoretical notions" .
"stones" .
"appendix" .
"study" .
"There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop\u00AD ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. 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 in the books of BIRKHOFF [2J and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know\u00AD ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs." .
_:N104182c9297b4e2d8d7cca541551709c "doi" .
_:N104182c9297b4e2d8d7cca541551709c "10.1007/978-3-642-85820-8" .
"kind" .
.
"Boolean Algebras" .
_:N41dafad172c54f7989a9c4f205b99ce0 "Springer Nature - SN SciGraph project" .
"paper" .
"Boolean algebra" .
"algebraic one" .
.
"point" .
"work" .
"aspects" .
"algebra" .
"Pure Mathematics" .
.
"field of sets" .
"fundamental theorem" .
"https://scigraph.springernature.com/explorer/license/" .
"chapter I" .
"generalization" .
"set" .
"1969" .
"book" .
.
"2022-05-10T10:34" .
.
"point of view" .
.
_:Ne76c16544f2e4dc8a62e1b06bf5a046a "Springer Nature" .
"new era" .
"book" .
"Mathematical Sciences" .
"view" .
"operation" .
"part" .
"H. Stone" .
"greater part" .
"one" .
"special kind" .
"Birkhoff" .
"algebraic" .
"978-3-642-85822-2" .
"ment" .
"false"^^ .
"books" .
_:N48d252079fe343bea76d2163aa96294f "dimensions_id" .
"era" .
"Boolean operations" .
"direction" .
"algebraic rings" .
.
_:N48d252079fe343bea76d2163aa96294f "pub.1045547780" .
_:Ne76c16544f2e4dc8a62e1b06bf5a046a .
.
"theory" .
_:Ne76c16544f2e4dc8a62e1b06bf5a046a .
"notion" .
"little mention" .
"theorem" .
"978-3-642-85820-8" .
"content" .
_:N41dafad172c54f7989a9c4f205b99ce0 .
.
_:N104182c9297b4e2d8d7cca541551709c .
"https://doi.org/10.1007/978-3-642-85820-8" .
_:N48d252079fe343bea76d2163aa96294f .
"ring" .
"mention" .
"chapter" .
.
"1969-01-01" .
_:N104182c9297b4e2d8d7cca541551709c .
_:N48d252079fe343bea76d2163aa96294f .
"field" .
"en" .