Frame quasi-uniformities by entourages

Jorge Picado
Departamento de Matemática
Universidade de Coimbra

Festschrift for G. C. L. Brümmer on his 60th birthday, Department of Mathematics, University of Cape Town, 1999, pp. 161-175

Abstract: In this paper we present a theory of quasi-uniformities for frames in terms of entourages, that is, special elements of the binary coproduct of the frame by itself, and we prove that this theory is equivalent to J.L. Frith's theory of covering quasi-uniformities [J.L. Frith, Structured frames, PhD Thesis, University of Cape Town, 1987]. For that we make use of the definitions and techniques introduced and developed in [J. Picado, Weil uniformities for frames, Comment. Math. Univ. Carolinae 36 (1995) 357-370].

Keywords: frame, biframe, quasi-uniform frame, C-ideal, frame coproduct, entourage, Weil quasi-uniform frame.

AMS Subject Classification: 06D20, 54E15, 54E55.