The congruence biframe as a quasi-uniform bicompletion

Abstract

Künzi and Ferrario have shown that a $T_0$ space is sober if and only if it is bicomplete in the well-monotone quasi-uniformity. We prove a pointfree version of this result: a strictly zero-dimensional biframe is a congruence biframe if and only if it is bicomplete in the same quasi-uniformity. As a corollary we obtain a new proof of a result of Plewe that a congruence frame is ultraparacompact. The main result makes use of a new construction of the bicompletion of a quasi-uniform biframe as a quotient of the Samuel compactification.

12 pages, 0 figures. To be published in Topology and its Applications

References in corpus (1)

• Strictly zero-dimensional biframes and a characterisation of congruence frames

Cited by in corpus (1)

• Uniform locales and their constructive aspects