Iztok Banič (Author), Matevž Črepnjak (Author), Goran Erceg (Author), Matej Merhar (Author), Uroš Milutinović (Author)

Abstract

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.

Keywords

topologija;inverzne limite;navzgor polzvezne funkcije;inducirane funkcije;inducirani morfizmi;ne zaključna dela;topology;inverse limits;upper semi-continuous functions;induced functions;induced morphisms;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 515.126
COBISS: 16625241 Link will open in a new window
ISSN: 2232-2094
Parent publication: Preprint series
Views: 1000
Downloads: 39
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: Slovenian
Secondary title: Induciranje funkcij med inverznimi limitami z navzgor polzveznimi veznimi funkcijami
Secondary abstract: 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.
Secondary keywords: Matematika;Topologija;Infinitezimalni račun;
URN: URN:SI:UM:
Type (COBISS): Article
Pages: str. 1-18
Volume: ǂVol. ǂ51
Issue: ǂšt. ǂ1186
Chronology: 2013
ID: 1476830