| Title:
|
Upper quasi continuous maps and quasi continuous selections (English) |
| Author:
|
Matejdes, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
517-525 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the existence of a quasi continuous selection of a multifunction for which upper inverse image of any open set with compact complement contains a set of the form $(G\setminus I)\cup J$, where $G$ is open and $I$, $J$ are from a given ideal. The methods are based on the properties of a minimal multifunction which is generated by a cluster process with respect to a system of subsets of the form $(G\setminus I)\cup J$. (English) |
| Keyword:
|
selection |
| Keyword:
|
quasi continuity |
| Keyword:
|
minimal usco multifunction |
| Keyword:
|
cluster point |
| Keyword:
|
generalized quasi continuity |
| MSC:
|
26E25 |
| MSC:
|
54C60 |
| MSC:
|
54C65 |
| idZBL:
|
Zbl 1224.54050 |
| idMR:
|
MR2657966 |
| . |
| Date available:
|
2010-07-20T16:55:26Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140586 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Ganguly, D. K., Chandrani, Mitra: Some remarks on $B^*$-continuous functions.Anal. St. Univ. Ali. Cuza, Isai 46 (2000), 331-336. MR 1880218 |
| Reference:
|
[4] Ganguly, D. K., Mallick, P.: On generalized continuous multifunctions and their selections.Real Anal. Exchange 33 (2007/2008), 449-456. MR 2458261 |
| Reference:
|
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| Reference:
|
[6] Holá, L., Holý, D.: Minimal usco maps, densely continuous forms and upper semicontinuous functions.Rocky Mount. J. Math. 39 (2009), 545-562. MR 2491151, 10.1216/RMJ-2009-39-2-545 |
| Reference:
|
[7] Holý, D., Matejíčka, L.: C-upper semicontinuous and C$^{*}$-upper semicontinuous multifunctions.Tatra Mount. Math. Publ. 34 (2006), 159-165. Zbl 1135.54009, MR 2287252 |
| Reference:
|
[8] Holý, D., Matejíčka, L.: Quasicontinuous functions, minimal USCO maps and topology of pointwise convergence.Math. Slovaca (accepted). MR 2660032 |
| Reference:
|
[9] Matejdes, M.: Sur les seléctors des multifunctions.Math. Slovaca 37 (1987), 111-124. MR 0899022 |
| Reference:
|
[10] Matejdes, M.: Continuity of multifunctions.Real Anal. Exchange 19 (1993-94), 394-413. MR 1282658, 10.2307/44152391 |
| Reference:
|
[11] Matejdes, M.: Minimality of multifunctions.Real Anal. Exchange 32 (2007), 519-526. Zbl 1138.54016, MR 2369860, 10.14321/realanalexch.32.2.0519 |
| Reference:
|
[12] Neubrunn, T.: C-continuity and closed graphs.Čas. pro pěst. mat. 110 (1985), 172-178. Zbl 0589.54027, MR 0796566 |
| Reference:
|
[13] Neubrunn, T.: Quasi continuity.Real Anal. Exchange 14 (1988-89), 259-306. MR 0995972 |
| . |
