Cauchy completions of uniform frames
by
D. Doitchinov
University of Sofia

One can consider two different notions of completeness of uniform frames. The first one is founded on some categorical reasons and is more often accepted now. (It is systematically investigated, for instance, in [1].) The other one is based on the notion of a Cauchy filter and we will use for it the term Cauchy completeness. As shown in [1], every "categorically" complete uniform frame is Cauchy complete, but not inversely. The purpose of this paper is to give a construction of a special Cauchy completion of a uniform frame.

As for the notion of a uniform frame itself, we use here, in a slightly modified version, its ëntourage" definition proposed in [3] which instead of coverings, earlier used for the same purpose, uses mappings of a special kind.

[1] B. Banaschewski and A. Pultr, Samuel compactification and completion of uniform frames, Math. Proc. Camb. Phil. Soc., 108 (1990), 63-78.

[2] Á. Czászár, Extensions of quasi-uniformities, Acta Math. Acad. Sci. Hungar., 37 (1981), 121-145.

[3] P. Fletcher and W. Hunsaker, Entourage uniformities for frames, Mh. Math., 112 (1991), 271-279.

[4] P. Samuel, Ultrafilters and compactifications of uniform spaces, Trans. Amer. Math. Soc., 64 (1948), 100-132.

Date received: July 10, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caaj-42.