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1.
Paths through inverse limits
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, 2009

Opis: 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.
Ključne besede: 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
Objavljeno: 10.07.2015; Ogledov: 447; Prenosov: 14
URL Povezava na celotno besedilo

2.
Towards the complete classification of tent maps inverse limits
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, 2010

Opis: We study tent map inverse limits, i.e. inverse limits of inverse sequences of unit segments ▫$I$▫ with a tent map being the only bonding function. As the main result we identify an infinite family of curves in ▫$I^2$▫ such that if top points of graphs of tent maps belong to the same curve, the corresponding inverse limits are homeomorphic, and if they belong to different curves, the inverse limits are non-homeomorphic. The inverse limits corresponding to certain families of top points are explicitly determined, and certain properties of the inverse limit are proved in the case of ▫$(0,1)$▫ as the top point.
Ključne besede: matematika, topologija, kontinuumi, inverzne limite, mathematics, topology, continua, inverse limits, tent maps, Knaster continua
Objavljeno: 10.07.2015; Ogledov: 331; Prenosov: 15
URL Povezava na celotno besedilo

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Tent maps inverse limits and open problems
Matevž Črepnjak, Iztok Banič, Matej Merhar, Uroš Milutinović, 2011, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: mathematics, topology, continua, inverse limits, tent maps, Knaster continua
Objavljeno: 07.06.2012; Ogledov: 634; Prenosov: 22
URL Povezava na celotno besedilo

6.
Limits of inverse limits and applications
Matej Merhar, Iztok Banič, Matevž Črepnjak, Uroš Milutinović, 2011, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: mathematics, topology, continua, inverse limits, upper semi-continuous set-valued functions
Objavljeno: 07.06.2012; Ogledov: 660; Prenosov: 12
URL Povezava na celotno besedilo

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Paths through inverse limits
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, 2011, izvirni znanstveni članek

Opis: In Banič, Črepnjak, Merhar and Milutinović (2010) [2] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions ▫$f_n : X to 2^X$▫ converges to the graph of a continuous single-valued function ▫$f : X to X$▫, 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. The result is also 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.
Ključne besede: mathematics, topology, continua, limits, inverse limits, upper semi-continuous set-valued functions, paths, arcs
Objavljeno: 07.06.2012; Ogledov: 792; Prenosov: 29
URL Povezava na celotno besedilo

10.
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