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Article

Dube, Themba
A short note on separable frames. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 37 (1996), issue 2, pp. 375-377
MSC: 06D20, 54D10 | MR 1399008 | Zbl 0849.54012
Keywords:
separable; metrizable; frame
Summary:
Following the introduction of separability in frames ([2]) we investigate further properties of this notion and establish some consequences of the Urysohn metrization theorem for frames that are frame counterparts of corresponding results in spaces. In particular we also show that regular subframes of compact metrizable frames are metrizable.
References:
[1] Banaschewski B., Pultr A.: Samuel compactification and completion of uniform frames. Math. Proc. Cambridge Phil. Soc. 108 (1990), 63-78. MR 1049760 | Zbl 0733.54020
[2] Dube T.: Separability in locales. Quaest. Math. 17 (1994), 333-338. MR 1290672 | Zbl 0816.54018
[3] Johnstone P.T.: Stone Spaces. Cambridge Univ. Press, Cambridge, 1982. MR 0698074 | Zbl 0586.54001
[4] Pultr A.: Remarks on metrizable locales. Suppl. Rend. Circ. Mat. Palermo 6 (1984), 247-258. MR 0782722 | Zbl 0565.54001
[5] Sun S.-H.: On paracompact locales and metric locales. Comment. Math. Univ. Carolinae 30 (1989), 101-107. MR 0995708 | Zbl 0691.06003
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