A note on semi-regular locales

Document Type: Research Paper

Author

Institute of Mathematics, Nanjing Normal University, Nanjing, 210097, China.

Abstract

Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.

Keywords


[1] B. Banaschewski and A. Pultr, Booleanization, Cahiers de Topologie et Geometrie Di erentielle Categoriques, 35 (1994), 227C237.
[2] J. Paseka and Smarda, Semiregular frames, Archiv Math. (Brno), 26 (1992), 223-228.
[3] T. Dube, Katetov rexisited: a frame-theoretic excursion, Quaes. Math. 30 (2007), 365-380.
[4] P.T.Johnstone, Stone Spaces, Cambridge University Press, Cambridge, 1982.
[5] P.T.Johnstone, Sketches of an elephant: A topos theory compendium, vol. 2, Oxford Science Publications, 2002.
[6] J. Porter and J. Thomas, On H-closed and minimal Hausdor spaces, Trans. A mer. Math. Soc. 138 (1969), 159-170.
[7] M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, On Semi-regualarization Topologies, J. Austral. Math. Soc. (Series A) 38 (1985), 40-54.
[8] R. Engelking, General Topology, Sigma Series in Pure Math, Vol.6, Berlin: Heldermann, 1989.