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;ne zaključna dela;poti;loki;mathematics;topology;continua;limits;inverse limits;upper semi-continuous set-valued functions;paths;arcs;

Data

Language: English
Year of publishing:
Typology: 0 - Not set
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
UDC: 515.126
COBISS: 15352409 Link will open in a new window
ISSN: 1318-4865
Views: 1325
Downloads: 76
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Other data

Secondary language: Unknown
Secondary keywords: Matematika;Topologija;Infinitezimalni račun;Funkcije (matematika);
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: str. 1-24
Volume: ǂVol. ǂ47
Issue: ǂšt. ǂ1107
Chronology: 2009
ID: 68033
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