Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
minimal usco map; convergence space; complete uniform convergence space; pointwise convergence; order convergence
minimal usco map; convergence space; complete uniform convergence space; pointwise convergence; order convergence
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.
References:
[1] Anguelov, R.: Dedekind order completion of C(X) by Hausdorff continuous functions. Quaestiones Mathematicae 27 (2004), 153-170. DOI 10.2989/16073600409486091 | MR 2091694 | Zbl 1062.54017
[2] Anguelov, R., Rosinger, E. E.: Solving Large Classes of Nonlinear Systems of PDE's. Computers and Mathematics with Applications 53 (2007), 491-507. DOI 10.1016/j.camwa.2006.02.040 | MR 2323705
[3] Anguelov, R., Rosinger, E. E.: Hausdorff Continuous Solutions of Nonlinear PDEs through the Order Completion Method. Quaestiones Mathematicae 28 (2005), 271-285. DOI 10.2989/16073600509486128 | MR 2164372
[4] Anguelov, R., Walt, J. H. van der: Order Convergence Structure on $C(X)$. Quaestiones Mathematicae 28 (2005), 425-457. DOI 10.2989/16073600509486139 | MR 2182453
[5] Beattie, R., Butzmann, H.-P.: Convergence structures and applications to functional analysis. Kluwer Academic Plublishers, Dordrecht, Boston, London (2002). MR 2327514
[6] Borwein, J., Kortezov, I.: Constructive minimal uscos. C.R. Bulgare Sci 57 (2004), 9-12. MR 2117234 | Zbl 1059.54019
[7] Fabian, M.: Gâteaux differentiability of convex functions and topology: weak Asplund spaces. Wiley-Interscience, New York (1997). MR 1461271 | Zbl 0883.46011
[8] Hansell, R. W., Jayne, J. E., Talagrand, M.: First class selectors for weakly upper semi-continuous multi-valued maps in Banach spaces. J. Reine Angew. Math. 361 (1985), 201-220. MR 0807260 | Zbl 0573.54012
[9] Luxemburg, W. A., Zaanen, A. C.: Riesz Spaces I. North-Holland, Amsterdam, London (1971).
[10] Kalenda, O.: Stegall compact spaces which are not fragmentable. Topol. Appl. 96 (1999), 121-132. DOI 10.1016/S0166-8641(98)00045-5 | MR 1702306 | Zbl 0991.54030
[11] Kalenda, O.: Baire-one mappings contained in a usco map. Comment. Math. Univ. Carolinae 48 (2007), 135-145. MR 2338835
[12] Sendov, B.: Hausdorff approximations. Kluwer Academic, Boston (1990). MR 1078632 | Zbl 0715.41001
[13] Spurný, J.: Banach space valued mappings of the first Baire class contained in usco mappings. Comment. Math. Univ. Carolinae 48 (2007), 269-272. MR 2338094
[14] Srivatsa, V. V.: Baire class 1 selectors for upper semicontinuous set-valued maps. Trans. Amer. Math. Soc. 337 (1993), 609-624. MR 1140919 | Zbl 0822.54017
Search
Partner of
