frame; locale; topological space; cover; dense cover
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.
 Dowker C.H., Strauss D.: Sums in the category of frames
. Houston J. Math. 3 (1976), 17-32. MR 0442900
| Zbl 0332.54005
 Kovár M.: Finitely Regular and Finitely Normal Topological Spaces (in Czech). Masaryk University, Brno, 1989.
 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
 Kunen K., Vaughan J.E.: Handbook of Set-Theoretic Topology
. North Holland, Amsterdam, 1984. MR 0776619
| Zbl 0674.54001
 Madden J., Vermeer J.: Lindelöf locales and realcompactness
. Math. Proc. Cambridge Philos. Soc. 99 (1986), 473-480. MR 0830360
| Zbl 0603.54021
 Paseka J.: Products in the category of locales: which properties are preserved?
. Discrete Mathematics 108 (1992), 63-73. MR 1189830
| Zbl 0759.18005