| Title:
|
On multifunctions with closed graphs (English) |
| Author:
|
Holý, D. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
779-786 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The set of points of upper semicontinuity of multi-valued mappings with a closed graph is studied. A topology on the space of multi-valued mappings with a closed graph is introduced. (English) |
| Keyword:
|
upper semicontinuity |
| Keyword:
|
multifunction |
| Keyword:
|
closed graph |
| Keyword:
|
$c$-upper semicontinuity |
| Keyword:
|
complete uniform space |
| MSC:
|
54B20 |
| MSC:
|
54C60 |
| idZBL:
|
Zbl 0995.54008 |
| idMR:
|
MR1869467 |
| DOI:
|
10.21136/MB.2001.134112 |
| . |
| Date available:
|
2009-09-24T21:56:49Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134112 |
| . |
| Reference:
|
[1] G. Beer: Topologies on closed and convex sets.Kluwer Academic Publishers, 1993. MR 1269778 |
| Reference:
|
[2] V. Baláž, Ľ. Holá, T. Neubrunn: Remarks on $c$-continuous.Acta Mathematica Univ. Com. L-LI (1987), 51–59. |
| Reference:
|
[3] S. Dolecki: Semicontinuity in constrained optimization II.Control Cybernet. 2 (1978), 5–16. MR 0641777 |
| Reference:
|
[4] S. Dolecki, A. Lechicki: On structure of upper semicontinuity.J. Math. Anal. Appl. 88 (1982), 547–554. MR 0667078, 10.1016/0022-247X(82)90213-X |
| Reference:
|
[5] R. Engelking: General Topology.PWN, Warszaw, 1977. Zbl 0373.54002, MR 0500780 |
| Reference:
|
[6] Z. Frolík: Generalizations of the $G_\delta $-property of complete metric spaces.Czechoslovak Math. J. 85 (1960). MR 0116305 |
| Reference:
|
[7] Ľ. Holá: An extension theorem for continuous functions.Czechoslovak Math. J. 113 (1988), 398–403. MR 0950293 |
| Reference:
|
[8] Ľ. Holá, I. Kupka: Closed graph and open mapping theorems for linear relations.Acta Mathematica Univ. Com. 46–47 (1985), 157–162. MR 0872338 |
| Reference:
|
[9] I. Kupka, V. Toma: Measure of noncompactness in topological spaces and upper semicontinuity of multifunctions.Rev. Roumaine Math. Pures Appl. 40 (1995), 455–461. MR 1404628 |
| Reference:
|
[10] A. Lechicki, S. Levi: Extension of semicontinuous multifunctions.Forum Math. (1990), 341–360. MR 1057877 |
| Reference:
|
[11] K. Sakálová: Continuity properties of multifunctions.Acta Mathematica Univ. Com. 56–57 (1989), 159–165. MR 1083019 |
| . |
