Completely regular proper reflection of locales over a given locale. (English) Zbl 1281.06007
Summary: 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 \(\mathrm{Loc}/X\) and the reflection map is a dense embedding if and only if \( Y\) is completely regular.
MSC:
| 06D22 | Frames, locales |
| 18B25 | Topoi |
| 54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
References:
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