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

Abstract

In [I.Banič, M. Črepnjak, M. Merhar, U. Milutinović, Limits of inverse limits, Topology Appl. 157 (2010) 439-450] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions ▫$f_n: X \rightarrow 2^X$▫ converges to the graph of a continuous single-valued function ▫$f: X \rightarrow X$▫, then the sequence of corresponding inverse limits obtained from ▫$f_n$▫ converges to the inverse limit obtained from ▫$f$▫. In this paper a more general result is presented in which surjectivity of ▫$f_n$▫ is not required. Also, the result is generalized to the case of inverse sequences with non-constant sequences of bonding maps. Finally, these new theorems are applied to inverse limits with tent maps. Among other applications it is shown that the inverse limits appearing in the Ingram conjecture (with a point added) form an arc.

Keywords

matematika;topologija;kontinuumi;limite;inverzne limite;navzgor polzvezne večlične funkcije;poti;loki;mathematics;topology;continua;limits;inverse limits;upper semi-continuous set-valued functions;paths;arcs;

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: 18474504 Link will open in a new window
ISSN: 0166-8641
Views: 1715
Downloads: 97
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Other data

Secondary language: Slovenian
Secondary keywords: matematika;topologija;kontinuumi;limite;inverzne limite;navzgor polzvezne večlične funkcije;poti;loki;
URN: URN:SI:UM:
Type (COBISS): Article
Pages: str. 1099-1112
Volume: ǂVol. ǂ158
Issue: ǂiss. ǂ9
Chronology: 2011
ID: 8723776
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