20.500.12556/DKUM-52016 Inverse limits in the category of compact Hausdorff spaces and upper semicontinuous functions Inverzne limite v kategoriji kompaktnih Hausdorffovih prostorov in navzgor polzveznih funkcij V članku obravnavamo inverzne limite v kategoriji ▫$mathcal{CHU}$▫ kompaktnih Hausdorffovih prostorov in navzgor polzveznih (u.s.c) preslikav. Vpeljemo pojem šibkih inverznih limit in pokažemo, da inverzne limite z navzgor polzveznimi veznimi preslikavami skupaj s projekcijami niso nujno inverzne limite v ▫$mathcal{CHU}$▫, so pa vedno šibke inverzne limite v tej kategoriji. Med drugim gre za realizacijo kategorijalnega pristopa k reševanju problema, ki ga je zastavil W. T. Ingram. We investigate inverse limits in the category ▫$mathcal{CHU}$▫ of compact Hausdorff spaces with upper semicontinuous (usc) functions. We introduce the notion of weak inverse limits in this category and show that the inverse limits with upper semicontinuous set-valued bonding functions (as they were defined in [W. T. Ingram, W. S.~Mahavier, Inverse limits of upper semi-continuous set valued functions, Houston J. Math. 32 (2006), 119--130]) together with the projections are not necessarily inverse limits in ▫$mathcal{CHU}$▫ but they are always weak inverse limits in this category. This is a realization of our categorical approach to solving a problem stated by W. T. Ingram in [W. T. Ingram, An Introduction to Inverse Limits with Set-valued Functions, Springer, New York etc., 2012]. topologija kategorije navzgor polzvezne funkcije inverzne limite posplošene inverzne limite šibke inverzne limite topology upper semi-continuous functions inverse limits generalized inverse limits weak inverse limits true true false Angleški jezik Slovenski jezik Članek v reviji 2015-07-10 15:33:31 2015-07-10 15:33:31 2024-03-15 14:22:28 2019-07-11 07:34:54 2013 0 0 str. 1-15 št. 1188 Vol. 51 2013 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.126 15706713 16625753 2232-2094 URN:SI:UM:DK:OCYY9TOT http://www.imfm.si/preprinti/PDF/01188.pdf 1 https://dk.um.si/Dokument.php?lang=slv&id=76576 Fakulteta za naravoslovje in matematiko 0 0 0