The Delta-Nielsen number in products

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dc.contributor.advisorSchlagbauer, Hen_ZA
dc.contributor.authorMordant, Ianen_ZA
dc.date.accessioned2016-10-21T07:32:52Z
dc.date.available2016-10-21T07:32:52Z
dc.date.issued1973en_ZA
dc.description.abstractIn 1967 Robert F. Brown derived a formula which relates the Nielsen number N(f) of a fibre map f to the Nielsen numbers N(f),(fb), where f,fb are induced by f. This work is concerned to prove an analogous result for the Δ-Nielsen number, N(f,g,Δ). In Chapter I we introduce the set of coincidences of two maps f,g: X->Γ,f(f,g) = {xϵX: f(x)=g(x)}. We partition this set into equivalence classes by means of the equivalence relation of fixed end-point homotopy and then study some of the geometry of the equivalence classes. We then proceed to introduce the Δ-Nielsen number N(f,g,Δ) by means of an index, which we show satisfies the axioms of Brooks [1969] for a coincidence index. Thereafter we show N(f,g,Δ) to be a homotopy invariant. In Chapter II we introduce the class of fibre spaces. By restricting ourselves to fibre spaces which are products of closed, finitely triangulable manifolds, we derive an analogous formula for coincidences as Brown has for fixed points. Some suggestions for a complete analogue conclude the work.en_ZA
dc.identifier.apacitationMordant, I. (1973). <i>The Delta-Nielsen number in products</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/22233en_ZA
dc.identifier.chicagocitationMordant, Ian. <i>"The Delta-Nielsen number in products."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1973. http://hdl.handle.net/11427/22233en_ZA
dc.identifier.citationMordant, I. 1973. The Delta-Nielsen number in products. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Mordant, Ian AB - In 1967 Robert F. Brown derived a formula which relates the Nielsen number N(f) of a fibre map f to the Nielsen numbers N(f),(fb), where f,fb are induced by f. This work is concerned to prove an analogous result for the Δ-Nielsen number, N(f,g,Δ). In Chapter I we introduce the set of coincidences of two maps f,g: X->Γ,f(f,g) = {xϵX: f(x)=g(x)}. We partition this set into equivalence classes by means of the equivalence relation of fixed end-point homotopy and then study some of the geometry of the equivalence classes. We then proceed to introduce the Δ-Nielsen number N(f,g,Δ) by means of an index, which we show satisfies the axioms of Brooks [1969] for a coincidence index. Thereafter we show N(f,g,Δ) to be a homotopy invariant. In Chapter II we introduce the class of fibre spaces. By restricting ourselves to fibre spaces which are products of closed, finitely triangulable manifolds, we derive an analogous formula for coincidences as Brown has for fixed points. Some suggestions for a complete analogue conclude the work. DA - 1973 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1973 T1 - The Delta-Nielsen number in products TI - The Delta-Nielsen number in products UR - http://hdl.handle.net/11427/22233 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22233
dc.identifier.vancouvercitationMordant I. The Delta-Nielsen number in products. [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/11427/22233en_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.titleThe Delta-Nielsen number in productsen_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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