On multifunctions with closed graphs

D. Holý

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 4, page 779-786
  • ISSN: 0862-7959

Abstract

top
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.

How to cite

top

Holý, D.. "On multifunctions with closed graphs." Mathematica Bohemica 126.4 (2001): 779-786. <http://eudml.org/doc/248878>.

@article{Holý2001,
abstract = {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.},
author = {Holý, D.},
journal = {Mathematica Bohemica},
keywords = {upper semicontinuity; multifunction; closed graph; $c$-upper semicontinuity; complete uniform space; upper semicontinuity; multifunction; closed graph; -upper semicontinuity; complete uniform space},
language = {eng},
number = {4},
pages = {779-786},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On multifunctions with closed graphs},
url = {http://eudml.org/doc/248878},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Holý, D.
TI - On multifunctions with closed graphs
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 4
SP - 779
EP - 786
AB - 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.
LA - eng
KW - upper semicontinuity; multifunction; closed graph; $c$-upper semicontinuity; complete uniform space; upper semicontinuity; multifunction; closed graph; -upper semicontinuity; complete uniform space
UR - http://eudml.org/doc/248878
ER -

References

top
  1. Topologies on closed and convex sets, Kluwer Academic Publishers, 1993. (1993) MR1269778
  2. Remarks on c -continuous, Acta Mathematica Univ. Com. L-LI (1987), 51–59. (1987) 
  3. Semicontinuity in constrained optimization II, Control Cybernet. 2 (1978), 5–16. (1978) MR0641777
  4. 10.1016/0022-247X(82)90213-X, J. Math. Anal. Appl. 88 (1982), 547–554. (1982) MR0667078DOI10.1016/0022-247X(82)90213-X
  5. General Topology, PWN, Warszaw, 1977. (1977) Zbl0373.54002MR0500780
  6. Generalizations of the G δ -property of complete metric spaces, Czechoslovak Math. J. 85 (1960). (1960) MR0116305
  7. An extension theorem for continuous functions, Czechoslovak Math. J. 113 (1988), 398–403. (1988) MR0950293
  8. Closed graph and open mapping theorems for linear relations, Acta Mathematica Univ. Com. 46–47 (1985), 157–162. (1985) MR0872338
  9. Measure of noncompactness in topological spaces and upper semicontinuity of multifunctions, Rev. Roumaine Math. Pures Appl. 40 (1995), 455–461. (1995) MR1404628
  10. Extension of semicontinuous multifunctions, Forum Math. (1990), 341–360. (1990) MR1057877
  11. Continuity properties of multifunctions, Acta Mathematica Univ. Com. 56–57 (1989), 159–165. (1989) MR1083019

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.