Posplošitve markovskih funkcij in njihove inverzne limite : doktorska disertacija

slovenian

doktorska dela

2018

countably Markov function   dissertations   function of the shape N   generalized Markov function   inverse limit   Markov interval map   set-valued function   tent function   upper semi-continuous function

Univerza v Mariboru, Fakulteta za naravoslovje in matematiko

The doctoral dissertation studies special types of generalized inverse limits. In the dissertation we successfully solved the problem of a good choise for the definition of generalized Markov functions and the definition of the same pattern of two such functions, which enables us to prove an analogue Theorem as in 11 for set-valued functions. Holte's Theorem refers only to surjective single-valued Markov functions. Our Theorem refers to set-valued functions, even without the assumption of surjectivity. Markov functions as well as ours, generalized Markov functions, have finite partitions. In the next part of the doctoral dissertation we have proven, that a further generalization is possible, where the partitions are countable infinite. With this we introduced countably Markov functions and the same pattern of two such functions. These two definitions have been created to enable us to prove the Theorem of homeomorficness of generalized inverse limits when the bonding functions are countably Markov functions with the same pattern. This theorem has also been proven without the assumption of surjectivity. We have applied this Theory to tent functions and functions of the shape N (two special types of single-valued and set-valued functions). In the last chapter we introduced some open problems.

08.08.2023