A note on semi-regular locales



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 re
ection or core


locale, semi-regular locale, semi-regularization. Subject Classication[2000]: 06D22, 54D10. Project supported by NSFC (11171156).

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B. Banaschewski and A. Pultr, Booleanization, Cahiers de Topologie et Geometrie

Dierentielle Categoriques, 35 (1994), 227C237.

T. Dube, Katetov rexisited: a frame-theoretic excursion, Quaes. Math. 30

(2007), 365-380.

R. Engelking, General Topology, Sigma Series in Pure Math, Vol.6, Berlin:

Heldermann, 1989.

P.T. Johnstone, Stone Spaces, Cambridge University Press, Cambridge, 1982.

P.T. Johnstone, Sketches of an elephant: A topos theory compendium, vol. 2,

Oxford Science Publications, 2002.

M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, On Semi-regualarization

Topologies, J. Austral. Math. Soc. (Series A) 38 (1985), 40-54.

J. Paseka and Smarda, Semiregular frames, Archiv Math. (Brno), 26 (1992),


J. Porter and J. Thomas, On H-closed and minimal Hausdor spaces, Trans.

A mer. Math. Soc. 138 (1969), 159-170.

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


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