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Frame quasi-uniformities. (English) Zbl 0796.54037
The authors introduce quasi-uniform locales and develop the theory as preliminary to their investigation of totally bounded quasi-uniform locales (or frames) in [Comment. Math. Univ. Carolin. 34, No. 3, 529-537 (1993; Zbl 0786.54028)].

MSC:
54E15 Uniform structures and generalizations
18B35 Preorders, orders, domains and lattices (viewed as categories)
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References:
[1] Banaschewski, B., Brümmer, G. C. L.: Strong zero-dimensionality of biframes and bispaces. Quaestiones Math.13, 273-290 (1990). · Zbl 0722.54019
[2] Banaschewski, B., Brümmer, G. C. L., Hardie, K. A.: Biframes and bispaces. Quaestiones Math.6, 13-25 (1983). · Zbl 0513.06005
[3] Banaschewski, B., Pultr, A.: Samuel compactification and completion of uniform frames. Math. Proc. Camb. Phil. Soc. (1)108, 63-78 (1990). · Zbl 0733.54020
[4] Fletcher, P., Hunsaker, W.: Entourage uniformities for frames. Mh. Math.112, 271-279 (1991). · Zbl 0736.54023
[5] Fletcher, P., Hunsaker, W.: Symmetry conditions in terms of open sets. Topology Appl.45, 39-47 (1992). · Zbl 0766.54025
[6] Fletcher, P., Hunsaker, W.: Totally Bounded Uniformities for Frames. Topology Proc., to appear. · Zbl 0790.54032
[7] Fletcher, P., Hunsaker, W., Lindgren, W.: Characterizations of Frame Quasi-Uniformities. Quaestiones Math. to appear. · Zbl 0792.54026
[8] Fletcher, P., Lindgren, W.: Quasi-Uniform Spaces. New York: Marcel Dekker. 1982. · Zbl 0501.54018
[9] Frith, J. L.: Structured Frames. Ph.D. Thesis. Univ. Cape Town. 1987.
[10] Gantner, T. E., Steinlage, R. C.: Characterizations of quasi-uniformities. J. London Math. Soc. (2)5, 48-52 (1972). · Zbl 0241.54023
[11] Isbell, J. R.: Uniform Spaces. Mathematical Surveys. No. 12. Providence, R.I.: Amer. Math. Soc. 1964. · Zbl 0124.15601
[12] Johnstone, P. T.: Stone Spaces. Cambridge: Univ. Press. 1982.
[13] Johnstone, P. T.: A Constructive Theory of Uniform Locales, I: Uniform Covers, ?General Topology and Applications? (ed.S. J. Andima et al.) Marcel Dekker Lecture Notes in Pure and Applied Mathematics134, 179-193 (1991). · Zbl 0760.54019
[14] Nachbin, L.: Sur les espaces uniformes ordonnés. C.R. Acad. Sci. Paris226, 774-775 (1948). · Zbl 0030.37303
[15] Pultr, A.: Pointless uniformities I. Complete regularity. Comment Math. Univ. Carolin.25, 91-104 (1984). · Zbl 0543.54023
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