| Title:
|
Lower semicontinuous functions with values in a continuous lattice (English) |
| Author:
|
van Gool, Frans |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
505-523 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that for every continuous lattice there is a unique semiuniform structure generating both the order and the Lawson topology. The way below relation can be characterized with this uniform structure. These results are used to extend many of the analytical properties of real-valued l.s.c\. functions to l.s.c\. functions with values in a continuous lattice. The results of this paper have some applications in potential theory. (English) |
| Keyword:
|
continuous lattices |
| Keyword:
|
lower semicontinuous functions |
| Keyword:
|
potential theory |
| MSC:
|
06B30 |
| MSC:
|
06B35 |
| MSC:
|
31D05 |
| MSC:
|
54C08 |
| MSC:
|
54E15 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 0769.06005 |
| idMR:
|
MR1209292 |
| . |
| Date available:
|
2009-01-08T17:57:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118518 |
| . |
| Reference:
|
[1] Bliedtner J., Hansen W.: Potential Theory. An Analytic and Probabilistic Approach to Balayage.Springer-Verlag, Berlin, 1986. Zbl 0706.31001, MR 0850715 |
| Reference:
|
[2] Borwein J.M., Théra M.: Sandwich Theorems for Semicontinuous Operators.preprint, 1990. |
| Reference:
|
[3] Bourbaki N.: Topologie Générale, ch. IX.Hermann & Cie, Paris, 1948. MR 0027138 |
| Reference:
|
[4] Constantinescu C., Cornea A.: Potential Theory on Harmonic Spaces.Springer-Verlag, Berlin, 1972. Zbl 0248.31011, MR 0419799 |
| Reference:
|
[5] Fletcher P., Lindgren W.F.: Quasi-uniform spaces.Lecture Notes in Pure and Applied Mathematics 77, Marcel Dekker inc., New York, 1982. Zbl 0583.54017, MR 0660063 |
| Reference:
|
[6] Gerritse G.: Lattice-valued Semicontinuous Functions.Report 8532, Catholic University of Nijmegen, 1985. Zbl 0872.54010 |
| Reference:
|
[7] Gierz G., Hofmann K., Keimel K., Lawson J., Mislove M., Scott D.: A Compendium of Continuous Lattices.Springer-Verlag, Berlin, 1980. Zbl 0452.06001, MR 0614752 |
| Reference:
|
[8] van Gool F.A.: Non-linear Potential Theory.Preprint 606, University of Utrecht, 1990. |
| Reference:
|
[9] Holwerda H.: Closed Hypographs, Semicontinuity and the Topological Closed-graph Theorem: A unifying Approach.Report 8935, Catholic University of Nijmegen, 1989. |
| Reference:
|
[10] Katětov M.: On real-valued functions in topological spaces.Fundamenta Mathematicae 38 (1951), 85-91 Correction in Fund. Math. 40 (1953), 203-205. MR 0050264 |
| Reference:
|
[11] Nachbin L.: Topology and Order.Van Nostrand, Princeton, 1965. Zbl 0333.54002, MR 0219042 |
| Reference:
|
[12] Penot J.P., Théra M.: Semi-continuous mappings in general topology.Arch. Math. 38 (1982), 158-166. |
| Reference:
|
[13] Tong H.: Some characterizations of normal and perfectly normal spaces.Duke Math. J. 19 (1952), 289-292. Zbl 0046.16203, MR 0050265 |
| . |
