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Keywords:
frame; locale; isocompact; ${\rm cl}$-isocompact; fully ${\rm cl}$-isocompact
frame; locale; isocompact; ${\rm cl}$-isocompact; fully ${\rm cl}$-isocompact
Summary:
Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called ${\rm cl}$-isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.
References:
[1] Bacon, P.: The compactness of countably compact spaces. Pac. J. Math. 32 (1970), 587-592 \99999DOI99999 10.2140/pjm.1970.32.587 . DOI 10.2140/pjm.1970.32.587 | MR 0257975 | Zbl 0175.49503
[2] Banaschewski, B., Gilmour, C.: Pseudocompactness and the cozero part of a frame. Commentat. Math. Univ. Carol. 37 (1996), 577-587. MR 1426922 | Zbl 0881.54018
[3] Banaschewski, B., Gilmour, C.: Realcompactness and the cozero part of a frame. Appl. Categ. Struct. 9 (2001), 395-417 \99999DOI99999 10.1023/A:1011225712426 . MR 1847309 | Zbl 0978.54019
[4] Dube, T.: Characterizing realcompact locales via remainders. Georgian Math. J. 28 (2021), 59-72. DOI 10.1515/gmj-2019-2027 | MR 4234116 | Zbl 07394014
[5] Dube, T., Iliadis, S., Mill, J. van, Naidoo, I.: A pseudocompact completely regular frame which is not spatial. Order 31 (2014), 115-120 \99999DOI99999 10.1007/s11083-013-9291-7 . MR 3167759 | Zbl 1316.06010
[6] Dube, T., Naidoo, I., Ncube, C. N.: Isocompactness in the category of locales. Appl. Categ. Struct. 22 (2014), 727-739 \99999DOI99999 10.1007/s10485-013-9341-8 . MR 3275271 | Zbl 1323.06008
[7] García-Ferreira, S., Sanchis, M.: Projection maps and isocompactness. Quest. Answers Gen. Topology 19 (2001), 165-176. MR 1854730 | Zbl 1016.54016
[8] García, J. Gutiérrez, Picado, J.: On the parallel between normality and extremal disconnectedness. J. Pure Appl. Algebra 218 (2014), 784-803. DOI 10.1016/j.jpaa.2013.10.002 | MR 3149635 | Zbl 1296.06006
[9] Hasegawa, M.: On products of isocompact spaces. Mem. Osaka Kyoiku Univ. III Natur. Sci. Appl. Sci. 21 (1972), 213-216. MR 0328864
[10] Isbell, J.: Graduation and dimension in locales. Aspects of Topology London Mathematical Society Lecture Note Series 93. Cambridge University Press, Cambridge (1985), 195-210. MR 0787829 | Zbl 0555.54020
[11] Isbell, J., Kříž, I., Pultr, A., Rosický, J.: Remarks on localic groups. Categorical Algebra and its Applications Lecture Notes in Mathematics 1348. Springer, Berlin (1988), 154-172. DOI 10.1007/BFb0081357 | MR 0975968 | Zbl 0661.22003
[12] Johnstone, P. T.: Stone Spaces. Cambridge Studies in Advanced Mathematics 3. Cambridge University Press, Cambridge (1982). MR 0698074 | Zbl 0499.54001
[13] Picado, J., Pultr, A.: Frames and Locales: Topology without Points. Frontiers in Mathematics. Springer, Berlin (2012). DOI 10.1007/978-3-0348-0154-6 | MR 2868166 | Zbl 1231.06018
[14] Picado, J., Pultr, A., Tozzi, A.: Locales. Categorical Foundations: Special Topics in Order, Topology, Algebra and Sheaf Theory Encyclopedia of Mathematics and Its Applications 97. Cambridge University Press, Cambridge (2004), 49-101. MR 2056581 | Zbl 1080.06010
[15] Plewe, T.: Sublocale lattices. J. Pure Appl. Algebra 168 (2002), 309-326. DOI 10.1016/S0022-4049(01)00100-1 | MR 1887161 | Zbl 1004.18003
[16] Sakai, M.: On $CL$-isocompactness and weak Borel completeness. Tsukuba J. Math. 8 (1984), 377-382. DOI 10.21099/tkbjm/1496160049 | MR 0767968 | Zbl 0558.54015
[17] Walters-Wayland, J. L.: Completeness and Nearly Fine Uniform Frames: Doctoral Thesis. Catholic University of Louvain, Louvain (1995).
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