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dc.contributor.authorTyree, Alan L
dc.date.accessioned2013-04-11T21:11:52Z
dc.date.available2013-04-11T21:11:52Z
dc.date.issued1973
dc.identifier.urihttp://hdl.handle.net/10179/4280
dc.description.abstractA restricted version of the Tietze Theorem is that a continuous mapping of a closed subspace of a metric space ranging in a closed interval may be extended to a continuous function defined upon the whole metric space. This may be viewed as a property of the closed interval and is expressed by saying that the interval is an absolute extensor. Thus, absolute extensors may be viewed as a generalisation of real intervals, and many of the desirable properties of intervals have been generalised to the class of absolute extensors. In 1951, Dugundji showed that every convex subset of a locally convex linear topological space is an absolute extensor, thus dramatically extending the Tietze theorem. In this thesis, a class of subsets of a normed linear space is defined. This new class of sets includes the convex sets and it is shown that these new sets are also absolute extensors.en
dc.language.isoenen
dc.publisherMassey Universityen_US
dc.rightsThe Authoren_US
dc.subjectTheory of retractsen
dc.subjectTopological spacesen
dc.subjectMathematicsen
dc.titleA class of absolute retracts : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey Universityen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorMassey Universityen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (Ph.D.)en


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