| Title:
|
The convergence space of minimal usco mappings (English) |
| Author:
|
Anguelov, R. |
| Author:
|
Kalenda, O. F. K. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
101-128 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all continuous functions is also addressed. (English) |
| Keyword:
|
minimal usco map |
| Keyword:
|
convergence space |
| Keyword:
|
complete uniform convergence space |
| Keyword:
|
pointwise convergence |
| Keyword:
|
order convergence |
| MSC:
|
54A05 |
| MSC:
|
54C60 |
| MSC:
|
54E15 |
| idZBL:
|
Zbl 1224.54048 |
| idMR:
|
MR2486619 |
| . |
| Date available:
|
2010-07-20T14:55:12Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140467 |
| . |
| Reference:
|
[1] Anguelov, R.: Dedekind order completion of C(X) by Hausdorff continuous functions.Quaestiones Mathematicae 27 (2004), 153-170. Zbl 1062.54017, MR 2091694, 10.2989/16073600409486091 |
| Reference:
|
[2] Anguelov, R., Rosinger, E. E.: Solving Large Classes of Nonlinear Systems of PDE's.Computers and Mathematics with Applications 53 (2007), 491-507. MR 2323705, 10.1016/j.camwa.2006.02.040 |
| Reference:
|
[3] Anguelov, R., Rosinger, E. E.: Hausdorff Continuous Solutions of Nonlinear PDEs through the Order Completion Method.Quaestiones Mathematicae 28 (2005), 271-285. MR 2164372, 10.2989/16073600509486128 |
| Reference:
|
[4] Anguelov, R., Walt, J. H. van der: Order Convergence Structure on $C(X)$.Quaestiones Mathematicae 28 (2005), 425-457. MR 2182453, 10.2989/16073600509486139 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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[9] Luxemburg, W. A., Zaanen, A. C.: Riesz Spaces I.North-Holland, Amsterdam, London (1971). |
| Reference:
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| Reference:
|
[11] Kalenda, O.: Baire-one mappings contained in a usco map.Comment. Math. Univ. Carolinae 48 (2007), 135-145. MR 2338835 |
| Reference:
|
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| Reference:
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| Reference:
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| . |
