Order topology for l-algebras
by
A. Pulgarín
Universidad de Extremadura (Spain)
Coauthors: F. Montalvo, B. Requejo

Let A be an l-algebra (an R-algebra endowed with an order relationship compatible with its operations and for which it is a lattice). Then A is a vector lattice and we can consider on A the classical notion of ''order topology''; let us denote such topology by t_v.

In this work we considered a different notion of order topology on A associate by natural way to the structure of l-algebra; let us denote this topology by t_a. The inequality t_a <= t_v is always satisfied, and we verified with an example that can not occur the equality. The object of this work is the study of the properties of t_a in order to obtain results of caracterization of the topological algebra C_k(X) (= algebra of the real and continuous functions on a topological space X equipped with the topology of the uniform convergence on compact subsets).

Date received: February 23, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafw-26.