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Keywords:
frame; locale; topological space; cover; dense cover
frame; locale; topological space; cover; dense cover
Summary:
In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.
References:
[1] Dowker C.H., Strauss D.: Sums in the category of frames. Houston J. Math. 3 (1976), 17-32. MR 0442900 | Zbl 0332.54005
[2] Engelking R.: General Topology. Polish Scientific Publishers, Warsaw, 1977. MR 0500780 | Zbl 0684.54001
[3] Johnstone P.T.: Stone Spaces. Cambridge Univ. Press, Cambridge, 1982. MR 0698074 | Zbl 0586.54001
[4] Kovár M.: Finitely Regular and Finitely Normal Topological Spaces (in Czech). Masaryk University, Brno, 1989.
[5] Kříž I.: A constructive proof of the Tychonoff's theorem for locales. Comment. Math. Univ. Carolinae 26 (1985), 619-630. MR 0817832 | Zbl 0661.54027
[6] Kunen K., Vaughan J.E.: Handbook of Set-Theoretic Topology. North Holland, Amsterdam, 1984. MR 0776619 | Zbl 0674.54001
[7] Madden J., Vermeer J.: Lindelöf locales and realcompactness. Math. Proc. Cambridge Philos. Soc. 99 (1986), 473-480. MR 0830360 | Zbl 0603.54021
[8] Paseka J.: Products in the category of locales: which properties are preserved?. Discrete Mathematics 108 (1992), 63-73. MR 1189830 | Zbl 0759.18005
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