Original Article
Kyungpook Mathematical Journal 2006; 46(2): 189-200
Published online June 23, 2006
Copyright © Kyungpook Mathematical Journal.
The Semicontinuous Quasi-uniformity of a Frame
Maria Jo~{a}o Ferreira, Jorge Picado
Departamento de Matem´atica, Universidade de Coimbra, Apartado 3008, Coimbra, Portugal
The semicontinuous quasi-uniformity is known to be one of the most important examples of transitive quasi-uniformities. The aim of this paper is to show that various facts in classical topology connected with the semicontinuous quasi-uniformity and semicontinuous real functions may be easily extended to pointfree topology via a construction introduced by the authors in a previous paper. Several consequences are derived.
Keywords: frame, biframe, quasi-uniform frame, biframe of reals, semicontinuous real function, transitive quasi-uniformity, functorial quasi-uniformity, spectrum cover