| Title:
|
Conditions under which the least compactification of a regular continuous frame is perfect (English) |
| Author:
|
Baboolal, Dharmanand |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
505-515 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize those regular continuous frames for which the least compactification is a perfect compactification. Perfect compactifications are those compactifications of frames for which the right adjoint of the compactification map preserves disjoint binary joins. Essential to our characterization is the construction of the frame analog of the two-point compactification of a locally compact Hausdorff space, and the concept of remainder in a frame compactification. Indeed, one of the characterizations is that the remainder of the regular continuous frame in each of its compactifications is compact and connected. (English) |
| Keyword:
|
regular continuous frame |
| Keyword:
|
perfect compactification |
| MSC:
|
06B35 |
| MSC:
|
06D20 |
| MSC:
|
06D22 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 1265.06028 |
| idMR:
|
MR2990190 |
| DOI:
|
10.1007/s10587-012-0025-6 |
| . |
| Date available:
|
2012-06-08T09:49:42Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142842 |
| . |
| Reference:
|
[1] Aarts, J. M., Boas, P. Van Emde: Continua as remainders in compact extensions.Nieuw Arch. Wisk., III. Ser. 15 (1967), 34-37. MR 0214033 |
| Reference:
|
[2] Baboolal, D.: Perfect compactifications of frames.Czech. Math. J. 61(136) (2011), 845-861. MR 2853096, 10.1007/s10587-011-0032-z |
| Reference:
|
[3] Banaschewski, B.: Compactification of frames.Math. Nachr. 149 (1990), 105-115. Zbl 0722.54018, MR 1124796, 10.1002/mana.19901490107 |
| Reference:
|
[4] Johnstone, P. T.: Stone Spaces.Cambridge University Press Cambridge (1982). Zbl 0499.54001, MR 0698074 |
| Reference:
|
[5] Jung, C. F. K.: Locally compact spaces whose Alexandroff one-point compactifications are perfect.Colloq. Math. 27 (1973), 247-249. Zbl 0262.54015, MR 0326661, 10.4064/cm-27-2-247-249 |
| Reference:
|
[6] Sklyarenko, E. G.: Some questions in the theory of bicompactifications.Am. Math. Soc. Transl., II. Ser. 58 (1966), 216-244. 10.1090/trans2/058/11 |
| . |
