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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Massey University
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A 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.
Theory of retracts, Topological spaces, Mathematics