| Title:
|
On binary coproducts of frames (English) |
| Author:
|
Chen, Xiangdong |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
699-712 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The structure of binary coproducts in the category of frames is analyzed, and the results are then applied widely in the study of compactness, local compactness (continuous frames), separatedness, pushouts and closed frame homomorphisms. (English) |
| Keyword:
|
frame |
| Keyword:
|
binary coproduct |
| Keyword:
|
pushout |
| Keyword:
|
compactness |
| Keyword:
|
separatedness |
| Keyword:
|
continuous frame |
| Keyword:
|
closed homomorphism |
| Keyword:
|
$D(\kappa)$-frame |
| MSC:
|
06A15 |
| MSC:
|
06A23 |
| MSC:
|
18A20 |
| MSC:
|
18A30 |
| MSC:
|
54C10 |
| MSC:
|
54D10 |
| MSC:
|
54D30 |
| MSC:
|
54D45 |
| idZBL:
|
Zbl 0824.54004 |
| idMR:
|
MR1240192 |
| . |
| Date available:
|
2009-01-08T18:00:01Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118542 |
| . |
| Reference:
|
[1] Banaschewski B.: Bourbaki's fixpoint lemma reconsidered.Comment. Math. Univ. Carolinae 33 (1992), 303-309. Zbl 0779.06004, MR 1189661 |
| Reference:
|
[2] Banaschewski B.: On pushing out frames.Comment. Math. Univ. Carolinae 31 (1990), 13-21. Zbl 0706.18003, MR 1056165 |
| Reference:
|
[3] Banaschewski B.: Compactification of frames.Math. Nachr. 149 (1990), 105-116. Zbl 0722.54018, MR 1124796 |
| Reference:
|
[4] Banaschewski B.: Another look at the localic Tychonoff theorem.Comment. Math. Univ. Carolinae 26 (1985), 619-630. MR 0982782 |
| Reference:
|
[5] Bourbaki N.: Elements of Mathematics: General Topology.Reading, Mass.: Addison-Wesley, 1966. Zbl 1107.54001 |
| Reference:
|
[6] Chen X.: Closed Frame Homomorphisms.Doctoral Dissertation, McMaster University, 1991. Zbl 0858.54012 |
| Reference:
|
[7] Dowker C.H., Papert D.: Paracompact frames and closed maps.Symp. Math. 16 (1975), 93-116. Zbl 0324.54015, MR 0410663 |
| Reference:
|
[8] Dowker C.H., Strauss D.: Separation axioms for frames.Colloq. Math. Soc. János Bolyai 8 (1972), 223-240. MR 0394559 |
| Reference:
|
[9] Isbell J.R.: Atomless parts of spaces.Math. Scand. 31 (1972), 5-32. Zbl 0246.54028, MR 0358725 |
| Reference:
|
[10] Johnstone P.T.: Stone Space.Cambridge University Press, 1982. MR 0698074 |
| Reference:
|
[11] Kříž I., Pultr A.: Peculiar behaviour of connected locales.Cahiers de Top. et Géom. Diff. Cat. XXX-1 (1989), 25-43. MR 1000829 |
| Reference:
|
[12] Pultr A., Tozzi A.: Notes on Kuratowski-Mrówka theorems in point-free context.Cahiers de Top. et Géom. Diff. Cat. XXXIII-1 (1992), 3-14. Zbl 0772.54016, MR 1163423 |
| Reference:
|
[13] Vermeulen J.J.C.: Some constructive results related to compactness and the (strong) Hausdorff property for locales.Category Theory, Proceedings, Como 1990, Springer LNM 1488 (1991), 401-409. Zbl 0739.18001, MR 1173026 |
| . |
