zbMATH — the first resource for mathematics

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)].

54E15 Uniform structures and generalizations
18B35 Preorders, orders, domains and lattices (viewed as categories)
Full Text: DOI EuDML
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.