Upper quasi continuous maps and quasi continuous selections

Milan Matejdes

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 517-525
  • ISSN: 0011-4642

Abstract

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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 ∖ I ) ∪ 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 ∖ I ) ∪ J .

How to cite

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Matejdes, Milan. "Upper quasi continuous maps and quasi continuous selections." Czechoslovak Mathematical Journal 60.2 (2010): 517-525. <http://eudml.org/doc/38024>.

@article{Matejdes2010,
abstract = {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 $(G\setminus I)\cup J$.},
author = {Matejdes, Milan},
journal = {Czechoslovak Mathematical Journal},
keywords = {selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity; selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity},
language = {eng},
number = {2},
pages = {517-525},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Upper quasi continuous maps and quasi continuous selections},
url = {http://eudml.org/doc/38024},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Matejdes, Milan
TI - Upper quasi continuous maps and quasi continuous selections
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 517
EP - 525
AB - 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 $(G\setminus I)\cup J$.
LA - eng
KW - selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity; selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity
UR - http://eudml.org/doc/38024
ER -

References

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  6. Holá, L., Holý, D., 10.1216/RMJ-2009-39-2-545, Rocky Mount. J. Math. 39 (2009), 545-562. (2009) MR2491151DOI10.1216/RMJ-2009-39-2-545
  7. Holý, D., Matejíčka, L., C-upper semicontinuous and C * -upper semicontinuous multifunctions, Tatra Mount. Math. Publ. 34 (2006), 159-165. (2006) Zbl1135.54009MR2287252
  8. Holý, D., Matejíčka, L., Quasicontinuous functions, minimal USCO maps and topology of pointwise convergence, Math. Slovaca (accepted). MR2660032
  9. Matejdes, M., Sur les seléctors des multifunctions, Math. Slovaca 37 (1987), 111-124. (1987) MR0899022
  10. Matejdes, M., 10.2307/44152391, Real Anal. Exchange 19 (1993-94), 394-413. (1993) MR1282658DOI10.2307/44152391
  11. Matejdes, M., 10.14321/realanalexch.32.2.0519, Real Anal. Exchange 32 (2007), 519-526. (2007) Zbl1138.54016MR2369860DOI10.14321/realanalexch.32.2.0519
  12. Neubrunn, T., C-continuity and closed graphs, Čas. pro pěst. mat. 110 (1985), 172-178. (1985) Zbl0589.54027MR0796566
  13. Neubrunn, T., Quasi continuity, Real Anal. Exchange 14 (1988-89), 259-306. (1988) MR0995972

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