Paper read at the Symposium on Categorical Algebra and Topology University of Cape Town 29 June—3 July 1981

BIFRAMES AND BISPACES

Published in: Quaestiones Mathematicae
Volume 6 , issue 1-3 , 1983 , pages: 13–25

DOI: 10.1080/16073606.1983.9632289

Author(s): B. Banaschewski Banaschewski Department of Mathematical Sciences McMaster, Canada , G. , C.L. Brümmer Department of Mathematics, , K.A. Hardie Department of Mathematics,

Keywords: Primary 06D20 , 54E55 , secondary 18A40 , 54D10 , 54D30

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Abstract

The concept of a biframe is introduced. Then the known dual adjunction between topological spaces and frames (i.e. local lattices) is extended to one between bispaces (i.e. bitopological spaces) and biframes. The largest duality contained in this dual adjunction defines the sober bispaces, which are also characterized in terms of the sober spaces. The topological and the frame-theoretic concepts of regularity, complete regularity and compactness are extended to bispaces and biframes respectively. For the bispaces these concepts are found to coincide with those introduced earlier by J.C. Kelly, E.P. Lane, S. Salbany and others. The Stone-Čech compactification (compact regular coreflection) of a biframe is constructed without the Axiom of Choice.

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