20.500.12556/DKUM-52014 Inducing functions between inverse limits with upper semicontinuous bonding functions Induciranje funkcij med inverznimi limitami z navzgor polzveznimi veznimi funkcijami V članku predstavljamo kategorijo ▫$mathcal{CU}$▫, kjer so objekti kompaktni metrični prostori ▫$X$▫ morfizmi med njimi pa navzgor polzvezne preslikave iz ▫$X$▫ v ▫$2^Y$▫. Vpeljemo tudi kategorijo ▫$mathcal{ICU}$▫ inverznih zaporedij v ▫$mathcal{CU}$▫. Proučujemo inducirane funkcije med inverznimi limitami kompaktnih metričnih prostorov z navzgor polzveznimi veznimi funkcijami. Podamo kriterije za njihov obstoj in dokažemo imajo pod določenimi pogoji surjektivne grafe. Pokažemo tudi da predpis, ki objektom iz ▫$mathcal{ICU}$▫ priredi njihove inverzne limite, ki so objekti v ▫$mathcal{CU}$▫, morfizmom pa priredi inducirane preslikave ni funktor iz ▫$mathcal{ICU}$▫ v ▫$mathcal{CU}$▫, (je pa temu zelo blizu). Na koncu podamo še uporabno aplikacijo dokazanih rezultatov. In this paper we introduce the category ▫$mathcal{CU}$▫ in which the compact metric spaces are objects and upper semicontinuous functions from ▫$X$▫ to ▫$2^Y$▫ are morphisms from ▫$X$▫ to ▫$Y$▫. We also introduce the category ▫$mathcal{ICU}$▫ of inverse sequences in ▫$mathcal{CU}$▫. Then we investigate the induced functions between inverse limits of compact metric spaces with upper semicontinuous bonding functions. We provide criteria for their existence and prove that under suitable assumptions they have surjective graphs. We also show that taking such inverse limits is very close to being a functor (but is not a functor) from ▫$mathcal{ICU}$▫ to ▫$mathcal{CU}$▫, if morphisms are mapped to induced functions. At the end of the paper we give a useful application of the mentioned results. topologija inverzne limite navzgor polzvezne funkcije inducirane funkcije inducirani morfizmi topology inverse limits upper semi-continuous functions induced functions induced morphisms true true false Angleški jezik Slovenski jezik Članek v reviji 2015-07-10 15:33:28 2015-07-10 15:33:28 2024-03-15 14:29:10 2019-07-11 07:34:51 2013 0 0 str. 1-18 št. 1186 Vol. 51 2013 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.126 15706713 16625241 2232-2094 URN:SI:UM:DK:FKNT8AYT http://www.imfm.si/preprinti/PDF/01186.pdf 1 https://dk.um.si/Dokument.php?lang=slv&id=76574 Fakulteta za naravoslovje in matematiko 0 0 0