# Article

Full entry | PDF   (0.2 MB)
Keywords:
selection; quasi continuity; minimal usco multifunction; cluster point; generalized quasi continuity
Summary:
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\$.
References:
[1] Cao, J., Moors, W. B.: Quasicontinuous selections of upper continuous set-valued mappings. Real Anal. Exchange 31 (2005-2006), 63-71. MR 2218189
[2] Drewnowski, L., Labuda, I.: On minimal upper semicontinuous compact valued maps. Rocky Mount. J. Math. 20 (1990), 737-752. DOI 10.1216/rmjm/1181073096 | MR 1073720 | Zbl 0742.54006
[3] Ganguly, D. K., Chandrani, Mitra: Some remarks on \$B^*\$-continuous functions. Anal. St. Univ. Ali. Cuza, Isai 46 (2000), 331-336. MR 1880218
[4] Ganguly, D. K., Mallick, P.: On generalized continuous multifunctions and their selections. Real Anal. Exchange 33 (2007/2008), 449-456. MR 2458261
[5] Holá, L., Baláž, V., Neubrunn, T.: Remarks on \$c\$-continuous multifunctions. Acta Math. Univ. Comeniana L-LI (1987), 51-59. MR 0989403
[6] Holá, L., Holý, D.: Minimal usco maps, densely continuous forms and upper semicontinuous functions. Rocky Mount. J. Math. 39 (2009), 545-562. DOI 10.1216/RMJ-2009-39-2-545 | MR 2491151
[7] Holý, D., Matejíčka, L.: C-upper semicontinuous and C\$^{*}\$-upper semicontinuous multifunctions. Tatra Mount. Math. Publ. 34 (2006), 159-165. MR 2287252 | Zbl 1135.54009
[8] Holý, D., Matejíčka, L.: Quasicontinuous functions, minimal USCO maps and topology of pointwise convergence. Math. Slovaca (accepted). MR 2660032
[9] Matejdes, M.: Sur les seléctors des multifunctions. Math. Slovaca 37 (1987), 111-124. MR 0899022
[10] Matejdes, M.: Continuity of multifunctions. Real Anal. Exchange 19 (1993-94), 394-413. MR 1282658
[11] Matejdes, M.: Minimality of multifunctions. Real Anal. Exchange 32 (2007), 519-526. MR 2369860 | Zbl 1138.54016
[12] Neubrunn, T.: C-continuity and closed graphs. Čas. pro pěst. mat. 110 (1985), 172-178. MR 0796566 | Zbl 0589.54027
[13] Neubrunn, T.: Quasi continuity. Real Anal. Exchange 14 (1988-89), 259-306. MR 0995972

Partner of