Naslov
Generalized inverse limits and topological entropy

Autori
Erceg, Goran

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Prirodoslovno-matematički fakultet

Mjesto
Zagreb

Datum
30.09

Godina
2016

Stranica
103

Mentor
Matijević, Vlasta

Ključne riječi
category ; hyperspace ; inverse system ; inverse limit ; upper semicontinuous function ; generalized inverse limit ; Mahavier product ; topological entropy

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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