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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Completely regular proper reflection of locales over a given locale


Authors: Wei He and MaoKang Luo
Journal: Proc. Amer. Math. Soc. 141 (2013), 403-408
MSC (2010): Primary 06D22, 18B25, 54C10
Published electronically: June 5, 2012
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Abstract: Let $ X$ be a completely regular locale. We present a construction which shows that every locale $ f: Y \rightarrow X$ over $ X$ has a completely regular proper reflection in the slice category $ Loc/ X$ and the reflection map is a dense embedding if and only if $ Y$ is completely regular.


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Additional Information

Wei He
Affiliation: Institute of Mathematics, Nanjing Normal University, Nanjing, 210046, People’s Republic of China
Email: weihe@njnu.edu.cn

MaoKang Luo
Affiliation: Institute of Mathematics, Sichuan University, Chengdu, 610064, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11329-2
PII: S 0002-9939(2012)11329-2
Keywords: Locale, proper map, proper reflection
Received by editor(s): November 21, 2010
Received by editor(s) in revised form: May 4, 2011, and June 28, 2011
Published electronically: June 5, 2012
Additional Notes: This project was supported by NSF of China
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society