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13.
On strong approximations of usc nonconvex-valued mappings
Repovš, Dušan, 1954- ; Semenov, Pavel Vladimirovič, 1952-
Za poljubno navzgor polzvezno preslikavo ▫$F: X \to Y$▫ iz metričnega prostora ▫$X$▫ brez izoliranih točk v normiran prostor ▫$Y$▫ dokažemo obstoj enolične zvezne preslikave ▫$f: X \to Y$▫, za katero ...je Hausdorffova razdalja med grafoma ▫$\Gamma_F$▫ in ▫$\Gamma_f$▫ poljubno majhna, če ima "mera nekonveksnosti" vrednosti preslikave ▫$F$▫ primerno skupno zgornjo oceno. Tako dokažemo verzijo Beer-Cellinovega izreka pri pogoju kontrolirane opustitve konveksnosti vrednosti večličnih preslikav. Dani so tudi pogoji za tako krepko aproksimabilnost navzgor polzveznih preslikav z zvezdastimi vrednostmi v primerjavi z Beerovimi rezultati za Haudorffovo zvezne večlične preslikave z zvezdastimi vrednostmi.
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