Provider: DSpace RIS Export
Database: Massey Research Online (MRO) Production Instance
Content: text/plain; charset="UTF-8"
TY - THES
AB - 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.
N2 - 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.
M3 - Doctoral
PY - 1973
KW - Theory of retracts
KW - Topological spaces
KW - Mathematics
PB - Massey University
AU - Tyree, Alan L
TI - 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
LA - en
VL - Doctor of Philosophy (Ph.D.)
DA - 1973
UR - http://hdl.handle.net/10179/4280
ER -