Generalized inverse limits and topological entropy

Erceg, Goran (2016) Generalized inverse limits and topological entropy. Doctoral thesis, Faculty of Science > Department of Mathematics.

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Abstract

Generalized inverse limits are generalization of standard inverse limits in a way that in the corresponding inverse system bonding functions are upper semicontinuous (u.s.c.) functions instead of continuous functions. Concept was introduced in 2004 in [31] and later in 2006 in [28] and since then, theory has been developing rapidly. In the first part we introduce categories CHU and CU in which u.s.c. functions are morphisms and compact Hausdorff and compact metric spaces, respectively, are objects. We also introduce the category ICU of inverse sequences in CU. Then we investigate the induced functions between inverse limits of compact metric spaces with u.s.c. bonding functions. We also show that taking such inverse limits is very close to being a functor (but is not a functor) from ICU to CU, if morphisms are mapped to induced functions. At the end of the third chapter we give a useful application of the mentioned results. In the second part new definition of topological entropy is considered, in which is used Mahavier product, introduced in [19]. It is shown that new notion is well defined and that is in line with previous definitions for regular functions [41], using entropy of the shift map. Then, entropy of various examples is calculated, new ones and some well known. Finally, some new results about generalized inverse limits are shown using newly defined objects.

Item Type: Thesis (Doctoral thesis)
Keywords: category, hyperspace, inverse system, inverse limit, upper semicontinuous function, generalized inverse limit, Mahavier product, topological entropy
Supervisor: Kennedy, Judy and Matijević, Vlasta
Date: 2016
Number of Pages: 103
Subjects: NATURAL SCIENCES > Mathematics > Geometry and Topology
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 19 Oct 2016 09:13
Last Modified: 19 Oct 2016 09:13
URI: http://digre.pmf.unizg.hr/id/eprint/5178

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