## Completely regular proper reflection of locales over a given locale

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- by Wei He and MaoKang Luo PDF
- Proc. Amer. Math. Soc.
**141**(2013), 403-408 Request permission

## 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.## References

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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
- 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
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**141**(2013), 403-408 - MSC (2010): Primary 06D22, 18B25, 54C10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11329-2
- MathSciNet review: 2996945