Geodesic
Upper quasi continuous maps and quasi continuous selections
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 517-525.

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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 $(G\setminus I)\cup J$, 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 $(G\setminus I)\cup J$.
Classification : 26E25, 54C60, 54C65
Keywords: selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity 
@article{CMJ_2010__60_2_a16,
     author = {Matejdes, Milan},
     title = {Upper quasi continuous maps and quasi continuous selections},
     journal = {Czechoslovak Mathematical Journal},
     pages = {517--525},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {2010},
     mrnumber = {2657966},
     zbl = {1224.54050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a16/}
}
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Matejdes, Milan. Upper quasi continuous maps and quasi continuous selections. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 517-525. http://geodesic.mathdoc.fr/item/CMJ_2010__60_2_a16/