Stone algebra
Encyclopedia
In mathematics, a Stone algebra, or Stone lattice, is a pseudo-complemented distributive lattices such that a*∪a** = 1. They were introduced by and named after Marshall Harvey Stone
.
Boolean algebra
s are Stone algebras, and Stone algebras are Ockham algebra
s.
The open-set lattice of an extremally disconnected space
is a Stone algebra.
Marshall Harvey Stone
Marshall Harvey Stone was an American mathematician who contributed to real analysis, functional analysis, and the study of Boolean algebras.-Biography:...
.
Boolean algebra
Boolean algebra
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets...
s are Stone algebras, and Stone algebras are Ockham algebra
Ockham algebra
In mathematics, an Ockham algebra is a bounded distributive lattice with a dual endomorphism. They were introduced by , and were named after William of Ockham by ....
s.
The open-set lattice of an extremally disconnected space
Extremally disconnected space
In mathematics, a topological space is termed extremally disconnected or extremely disconnected if the closure of every open set in it is open. An extremally disconnected space that is also compact and Hausdorff is sometimes called a Stonean space...
is a Stone algebra.