| Title:
|
N-compact frames (English) |
| Author:
|
Schlitt, Greg M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
173-187 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate notions of $\Bbb N$-compactness for frames. We find that the analogues of equivalent conditions defining $\Bbb N$-compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame `$\Bbb N$-cubes' are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial $\Bbb N$-compactness form a much larger class, and better embody what `$\Bbb N$-compact frames' should be. This latter property is expressible without reference to maximal ideals or filters. We construct the co-reflections for both of the classes, (the `$\Bbb N$-compactifications'), which both restrict to the spatial $\Bbb N$-compactification. (English) |
| Keyword:
|
frame |
| Keyword:
|
locale |
| Keyword:
|
complete Heyting algebra |
| Keyword:
|
$\Bbb N$-compact |
| MSC:
|
06A23 |
| MSC:
|
06D20 |
| MSC:
|
06D99 |
| MSC:
|
18B30 |
| MSC:
|
54A05 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 0747.06009 |
| idMR:
|
MR1118300 |
| . |
| Date available:
|
2008-10-09T13:11:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116953 |
| . |
| Reference:
|
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