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: |
2013 |
Typology: |
1.01 - Original Scientific Article |
Organization: |
UM FNM - Faculty of Natural Sciences and Mathematics |
UDC: |
515.126 |
COBISS: |
16625753
|
ISSN: |
2232-2094 |
Parent publication: |
Preprint series
|
Views: |
26248 |
Downloads: |
93 |
Average score: |
0 (0 votes) |
Metadata: |
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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 |