Iztok Banič (Author), Tina Sovič (Author)

Abstract

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.

Keywords

topologija;kategorije;navzgor polzvezne funkcije;inverzne limite;posplošene inverzne limite;šibke inverzne limite;ne zaključna dela;topology;upper semi-continuous functions;inverse limits;generalized inverse limits;weak inverse limits;

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: 16625753 Link will open in a new window
ISSN: 2232-2094
Parent publication: Preprint series
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Other data

Secondary language: Slovenian
Secondary title: Inverzne limite v kategoriji kompaktnih Hausdorffovih prostorov in navzgor polzveznih funkcij
Secondary abstract: 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].
Secondary keywords: Matematika;Topologija;
URN: URN:SI:UM:
Type (COBISS): Article
Pages: str. 1-15
Volume: ǂVol. ǂ51
Issue: ǂšt. ǂ1188
Chronology: 2013
ID: 1476832