An approach to coincidence theory through universal covering spaces

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dc.contributor.advisorSchlagbauer, Hen_ZA
dc.contributor.authorHarvey, Duncan Reginald Arthuren_ZA
dc.date.accessioned2016-03-28T14:25:36Z
dc.date.available2016-03-28T14:25:36Z
dc.date.issued1973en_ZA
dc.description.abstractThe close relationship between the theory of fixed points and the theory of coincidences of maps is well known. This presentation is aimed at recording one of the less well documented approaches to fixed point theory as extended to the more general situation of coincidences. The approach referred to is that by way of the Universal Covering Spaces. The existing theory of coincidences is geometrically well realised in this setting and after some consideration, the necessary extensions and generalizations of the techniques as utilized in fixed point theory lead to an appealing conceptual notion of "essentiality of coincidence classes". Many hints have been made in the literature (see [1] and "On the sharpness of the Δ₂ and Δ₁ Nielsen Numbers" by Robin Brooks, J.Reine Angew. Math. 259, (1973), 101-108.) that lifts of mappings and the theory of fibres and related topics lend themselves to coincidence theory. It is the intention of this presentation to follow some of the basic properties through this approach and to show, wherever it is thought desirable, the ties between this and two of the existing approaches - for example, in the definition of the Nielsen Number, which is fundamental to both fixed point theory and coincidence theory.en_ZA
dc.identifier.apacitationHarvey, D. R. A. (1973). <i>An approach to coincidence theory through universal covering spaces</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18242en_ZA
dc.identifier.chicagocitationHarvey, Duncan Reginald Arthur. <i>"An approach to coincidence theory through universal covering spaces."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1973. http://hdl.handle.net/11427/18242en_ZA
dc.identifier.citationHarvey, D. 1973. An approach to coincidence theory through universal covering spaces. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Harvey, Duncan Reginald Arthur AB - The close relationship between the theory of fixed points and the theory of coincidences of maps is well known. This presentation is aimed at recording one of the less well documented approaches to fixed point theory as extended to the more general situation of coincidences. The approach referred to is that by way of the Universal Covering Spaces. The existing theory of coincidences is geometrically well realised in this setting and after some consideration, the necessary extensions and generalizations of the techniques as utilized in fixed point theory lead to an appealing conceptual notion of "essentiality of coincidence classes". Many hints have been made in the literature (see [1] and "On the sharpness of the Δ₂ and Δ₁ Nielsen Numbers" by Robin Brooks, J.Reine Angew. Math. 259, (1973), 101-108.) that lifts of mappings and the theory of fibres and related topics lend themselves to coincidence theory. It is the intention of this presentation to follow some of the basic properties through this approach and to show, wherever it is thought desirable, the ties between this and two of the existing approaches - for example, in the definition of the Nielsen Number, which is fundamental to both fixed point theory and coincidence theory. DA - 1973 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1973 T1 - An approach to coincidence theory through universal covering spaces TI - An approach to coincidence theory through universal covering spaces UR - http://hdl.handle.net/11427/18242 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/18242
dc.identifier.vancouvercitationHarvey DRA. An approach to coincidence theory through universal covering spaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1973 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/18242en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.subject.otherTopologyen_ZA
dc.titleAn approach to coincidence theory through universal covering spacesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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