A class of absolute retracts : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University

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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.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.identifier.urihttp://hdl.handle.net/10179/4280
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
massey.contributor.authorTyree, Alan Len
thesis.degree.disciplineMathematicsen
thesis.degree.grantorMassey Universityen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophy (Ph.D.)en
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