Abstract
New proofs of the characterization of paracompact frames as those frames which admit a complete uniformity, and of the existence of the paracompact regular reflection, based on the Samuel type completion, is presented.
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B. Banaschewski: Another look at the localic Tychonoff Theorem,Comment. Math. Univ. Carolinae 29 (1988), 647–656.
B. Banaschewski: Compactification of frames,Math. Nachr. 149 (1990), 105–116.
B. Banaschewski and G. C. L. Brümmer: Strong zero-dimensionaly and uniform rames, Unpublished manuscript.
B. Banaschewski and A. Pultr: Cauchy points of metric locales,Can. J. Math. 41 (1989), 830–854.
B. Banaschewski and A. Pultr: Samuel compactification and completion of uniform frames,Math. Proc. Cambridge Phil. Soc. 108 (1990), 63–78.
N. Bourbaki:Topologie Générale. Chapter IX, Exercises for §1, 21)e), Hermann & Cie, Paris.
E. Hewitt: Rings of real-valued continuous functions,Trans. Amer. Math. Soc. 64 (1948), 54–99.
J. R. Isbell:Uniform Spaces, Mathematical Surveys No. 12, Amer. Math. Society (1964).
J. R. Isbell: Atomless parts of spaces,Math. Scand. 31 (1972), 5–32.
P.T. Johnstone:Stone Spaces, Cambridge University Press, Cambridge (1982).
I. Kriz: A direct description of uniform completion in locales and a characterization ofLT groups,Cah. Top. et Géom. Diff. Cat. 27 (1986), 19–34.
A. Pultr: Pointless uniformities I. Complete regularity,Comment. Math. Univ. Carolinae 25 (1984), 91–104.
A. Pultr and J. Úlehla: Notes on characterization of paracompact frames,Comment. Math. Univ. Carolinae 30 (1989), 377–384.
S. H. Sun: On paracompact locales and metric locales,Comment. Math. Univ. Carolinae 30 (1989), 101–107.
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Banaschewski, B., Pultr, A. Paracompactness revisited. Appl Categor Struct 1, 181–190 (1993). https://doi.org/10.1007/BF00880042
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DOI: https://doi.org/10.1007/BF00880042