Some Properties of Certain Subsets of Infinite Dimensional Spaces.
William Barit · 1971
In this dissertation ve investigate some properties of certain subsets of infinite dimensional spaces.Results in three general areas are obtained.The first area concerns the extension of homeomorphisms between special subsets of Hilbert space.An £ -homeomorphisms extension theorem is proved which shows that small homeomorphisms between these subsets can be extended to space homeomorphisms.Results in the second area concern properties which most of the commonly studied infinite dimensional spaces do not have, These properties include having points which are not negligible, being non-homogeneousf and having no non-degenerate factors.Certain remainders of compactifications of infinite dimensional spaces are shown to possess these properties.The last area concerns contractibility.Certain subsets of the space of homeomorphisms of some infinite dimensional spaces are shown to be contractible.