| Title:
|
Sublocale sets and sublocale lattices (English) |
| Author:
|
Picado, Jorge |
| Author:
|
Pultr, Aleš |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
409-418 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present very short and simple proofs of such facts as co-frame distributivity of sublocales, zero-dimensionality of the resulting co-frames, Isbell’s Density Theorem and characteristic properties of fit and subfit frames, using sublocale sets. (English) |
| Keyword:
|
frames |
| Keyword:
|
sublocales |
| Keyword:
|
coframe of sublocales |
| Keyword:
|
fitness and subfitness |
| MSC:
|
06D22 |
| idZBL:
|
Zbl 1164.06313 |
| idMR:
|
MR2283021 |
| . |
| Date available:
|
2008-06-06T22:48:57Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108016 |
| . |
| Reference:
|
[1] Davey B. A., Priestley H. A.: Introduction to Lattices and Order.Second Edition, Cambridge University Press, 2001. Zbl 1002.06001, MR 1902334 |
| Reference:
|
[2] Isbell J. R.: Atomless parts of spaces.Math. Scand. 31 (1972), 5–32. Zbl 0246.54028, MR 0358725 |
| Reference:
|
[3] Johnstone P. T.: Stone Spaces.Cambridge Stud. Adv. Math. No 3, Cambridge University Press, 1983. MR 0698074 |
| Reference:
|
[4] Mac Lane S.: Categories for the Working Mathematician.Springer-Verlag, New York, 1971. Zbl 0232.18001, MR 0354798 |
| Reference:
|
[5] Picado J., Pultr A., Tozzi A.: Locales.In: M. C. Pedicchio and W. Tholen (Eds.), Categorical Foundations - Special Topics in Order, Topology, Algebra and Sheaf Theory, Encyclopedia of Mathematics and its Applications, Vol. 97, Cambridge University Press, 2003, pp. 49–101. Zbl 1080.06010, MR 2056581 |
| Reference:
|
[6] Priestley H. A.: Representation of distributive lattices by means of ordered Stone spaces.Bull. London Math. Soc. 2 (1970), 186–190. Zbl 0201.01802, MR 0265242 |
| Reference:
|
[7] Priestley H. A.: Ordered topological spaces and the representation of distributive lattices.Proc. London Math. Soc. 324 (1972), 507–530. Zbl 0323.06011, MR 0300949 |
| Reference:
|
[8] Pultr A., Sichler J.: Frames in Priestley duality.Cahiers Topologie Géom. Différentielle Catég. XXIX (1988), 193–202. MR 0975372 |
| Reference:
|
[9] Pultr A., Sichler J.: A Priestley view of spatialization of frames.Cahiers Topologie Géom. Différentielle Catég. XLI (2000), 225–238. Zbl 0970.06006, MR 1784219 |
| Reference:
|
[10] Simmons H.: The lattice theoretic part of topological separation properties.Proc. Edinburgh Math. Soc. (2) 21 (1978), 41–48. Zbl 0396.54014, MR 0493959 |
| . |
