Paths through inverse limits |
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Authors: | Iztok Bani? Matev? ?repnjak Matej Merhar |
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Institution: | a Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, Maribor 2000, Slovenia b Faculty of Chemistry and Chemical Engineering, Smetanova 17, 2000 Maribor, Slovenia c Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | In Bani?, ?repnjak, Merhar and Milutinovi? (2010) 2] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions fn:X→X2 converges to the graph of a continuous single-valued function f:X→X, then the sequence of corresponding inverse limits obtained from fn converges to the inverse limit obtained from f. In this paper a more general result is presented in which surjectivity of fn 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. |
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Keywords: | 54C60 54B10 54D80 54F65 54B99 |
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