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Title: Abstract topological dynamics
Author: Ahmed, Amna Mohamed Abdelgader
ISNI:       0000 0004 2717 9450
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2012
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Let \(\char{cmmi10}{0x54}\) : \(\char{cmmi10}{0x58}\) → \(\char{cmmi10}{0x58}\) be a function from a countably infinite set \(\char{cmmi10}{0x58}\) to itself. We consider the following problem: can we put a structure on \(\char{cmmi10}{0x58}\) with respect to which \(\char{cmmi10}{0x54}\) has some meaning? In this thesis, the following questions are addressed: when can we endow \(\char{cmmi10}{0x58}\) with a topology such that \(\char{cmmi10}{0x58}\) is homeomorphic to the rationals \(\char{msbm10}{0x51}\) and with respect to which \(\char{cmmi10}{0x54}\) is continuous? We characterize such functions on the rational world. The other question is: can we put an order on \(\char{cmmi10}{0x58}\) with respect to which \(\char{cmmi10}{0x58}\) is order-isomorphic to the rationals \(\char{msbm10}{0x51}\), naturals \(\char{msbm10}{0x4e}\) or integers \(\char{msbm10}{0x5a}\) with their usual orders and with respect to which \(\char{cmmi10}{0x54}\) is order-preserving (or order-reversing)? We give characterization of such bijections, injections and surjections on the rational world and of arbitrary maps on the naturals and integers in terms of the orbit structure of the map concerned.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: BC Logic ; QA Mathematics