The semicontinuous quasi-uniformity of a frame

• Author(s): Ferreira, Maria João ; Picado, Jorge
• Date: 2003
• Persistent ID: http://hdl.handle.net/10316/11427
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Frames; Biframes; Weil entourages; Quasi-uniform frames; Transitive quasi-uniformities; Totally bounded quasi-uniformities; Functorial quasi-uniformities; Fletcher construction; Spectrum covers; Biframe of reals; Semicontinuous real functions
• Document Type: Preprint
• Language: English

Description

The aim of this note is to show how various facts in classical topology connected with semicontinuous functions and the semicontinuous quasi-uniformity have their counterparts in pointfree topology. In particular, we introduce the localic semicontinuous quasi-uniformity, which generalizes the semicontinuous quasiuniformity of a topological space (known to be one of the most important examples of transitive compatible quasi-uniformities). We show that it can be characterized in terms of the so called spectrum covers, via a construction introduced by the authors in a previous paper. Several consequences are derived. Centro de Matemática da Universidade de Coimbra/FCT