Generalized Lattices

By: B Dvalishvili (Editor)

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Hardcover | 1 December 2004

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181 Pages

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If, presumably, the definition of a Boolean algebra employs the notion of a partially ordered set, whereas a general definition of a topological space is based on the notion of a metric, then by considering a more general situation with quasi metrics one may obtain the notion of a bitopological space (i.e., a set endowed with two arbitrary topologies). A further development of the theory of bitopological spaces has made it possible to introduce and study an algebra of a new type that is based on a nonordinary variant of a quasi ordered set and the corresponding representation of which brings one to bitopological spaces. The author calls this a generalised Boolean algebra, which is interesting not only as the subject of independent research, but also can be used as an important tool in establishing its various relationships with other areas of mathematics and, in particular, as in related double Boolean algebras with mathematical studies.

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Introduction and useful facts	p. 1
Gosets, generalized lattices, generalized Boolean algebras and the corresponding operations	p. 7
Generalized ideals and their variety : Stone family of prime generalized ideals	p. 71
Generalized filters and their variety : generalized duality between generalized ideals and generalized filters	p. 95
Generalized homomorphisms and generalized isomorphisms	p. 105
(i,j)-atoms and (i,j)-atomic generalized Boolean algebras	p. 117
Generalized Boolean factor algebras	p. 125
Generalized fields of sets and the generalized field representation of a generalized Boolean algebra	p. 133
Bitopological representation of a generalized Boolean algebra	p. 145
Generalized Boolean rings	p. 163
Table of Contents provided by Blackwell. All Rights Reserved.

Generalized Lattices

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Hardcover

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