The semicontinuous frame quasi-uniformity, revisited

• Author(s): Ferreira, Maria João ; Picado, Jorge
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/13649
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Frame; Quasi-uniform frame; Quasi-uniform biframe; Quasi-metric quasiuniformity; Totally bounded quasi-uniformity; Semicontinuous real function; Biframe of reals; Countably compact frame
• Document Type: Preprint
• Language: English

Description

In this note we present a new treatment of the pointfree version of the semicontinuous quasi-uniformity based on the new tool of the ring of arbitrary (not necessarily continuous) real-valued functions made available recently by J. Guti errez Garc a, T. Kubiak and J. Picado [Localic real functions: a general setting, Journal of Pure and Applied Algebra 213 (2009) 1064-1074]. The purpose is to show how the basic facts about the semicontinuous quasi-uniformity can be easily presented and proved with that tool at hand.