The convergence space of minimal usco mappings

R. Anguelov; O. F. K. Kalenda

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 1, page 101-128
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Anguelov, R., and Kalenda, O. F. K.. "The convergence space of minimal usco mappings." Czechoslovak Mathematical Journal 59.1 (2009): 101-128. <http://eudml.org/doc/37911>.

@article{Anguelov2009,
abstract = {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.},
author = {Anguelov, R., Kalenda, O. F. K.},
journal = {Czechoslovak Mathematical Journal},
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},
language = {eng},
number = {1},
pages = {101-128},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The convergence space of minimal usco mappings},
url = {http://eudml.org/doc/37911},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Anguelov, R.
AU - Kalenda, O. F. K.
TI - The convergence space of minimal usco mappings
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 101
EP - 128
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/37911
ER -

References

top
  1. Anguelov, R., 10.2989/16073600409486091, Quaestiones Mathematicae 27 (2004), 153-170. (2004) Zbl1062.54017MR2091694DOI10.2989/16073600409486091
  2. Anguelov, R., Rosinger, E. E., 10.1016/j.camwa.2006.02.040, Computers and Mathematics with Applications 53 (2007), 491-507. (2007) MR2323705DOI10.1016/j.camwa.2006.02.040
  3. Anguelov, R., Rosinger, E. E., 10.2989/16073600509486128, Quaestiones Mathematicae 28 (2005), 271-285. (2005) MR2164372DOI10.2989/16073600509486128
  4. Anguelov, R., Walt, J. H. van der, 10.2989/16073600509486139, Quaestiones Mathematicae 28 (2005), 425-457. (2005) MR2182453DOI10.2989/16073600509486139
  5. Beattie, R., Butzmann, H.-P., Convergence structures and applications to functional analysis, Kluwer Academic Plublishers, Dordrecht, Boston, London (2002). (2002) MR2327514
  6. Borwein, J., Kortezov, I., Constructive minimal uscos, C.R. Bulgare Sci 57 (2004), 9-12. (2004) Zbl1059.54019MR2117234
  7. Fabian, M., Gâteaux differentiability of convex functions and topology: weak Asplund spaces, Wiley-Interscience, New York (1997). (1997) Zbl0883.46011MR1461271
  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. (1985) Zbl0573.54012MR0807260
  9. Luxemburg, W. A., Zaanen, A. C., Riesz Spaces I, North-Holland, Amsterdam, London (1971). (1971) 
  10. Kalenda, O., 10.1016/S0166-8641(98)00045-5, Topol. Appl. 96 (1999), 121-132. (1999) Zbl0991.54030MR1702306DOI10.1016/S0166-8641(98)00045-5
  11. Kalenda, O., Baire-one mappings contained in a usco map, Comment. Math. Univ. Carolinae 48 (2007), 135-145. (2007) MR2338835
  12. Sendov, B., Hausdorff approximations, Kluwer Academic, Boston (1990). (1990) Zbl0715.41001MR1078632
  13. Spurný, J., Banach space valued mappings of the first Baire class contained in usco mappings, Comment. Math. Univ. Carolinae 48 (2007), 269-272. (2007) MR2338094
  14. Srivatsa, V. V., Baire class 1 selectors for upper semicontinuous set-valued maps, Trans. Amer. Math. Soc. 337 (1993), 609-624. (1993) Zbl0822.54017MR1140919

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.