Topological representation of double Boolean algebras

Topological Representation of Algebras

The Representation of Boolean Algebras

1. Introduction. In this brief address I shall set myself a twofold aim: to review the theory of Boolean algebras, as we understand it today, and to sketch certain historical phases of its development. Although I am in no sense prepared to offer the fruits of painstaking historical research, I believe that by a few pertinent historical observations I shall be able to bring out the underlying ev...

Topological Representation of Precontact Algebras

The notions of 2-precontact and 2-contact spaces as well as of extensional (and other kinds) 3-precontact and 3-contact spaces are introduced. Using them, new representation theorems for the precontact and contact algebras (satisfying some additional axioms) are proved. They incorporate and strengthen both the discrete and topological representation theorems from [3, 1, 2, 4, 10]. It is shown t...

Double Multipliers on Topological Algebras

The main purpose of this paper is to investigate some topological properties of the double multiplier algebra on a topological algebra. Let Md(A) be the double multiplier algebra on a topological algebra A, and let u and s be the uniform and strong operator topologies on Md(A), respectively. It is shown, under some additional hypotheses on A, that (1) Md(A) is uand s-complete; (2) A is a u-clos...

A representation theorem for Boolean contact algebras

We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [20] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T1 spaces.