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Metric Half-Spaces

This paper is a study of some of the basic properties of the metric half-space topology, a topology on a set which is derived from a metric on the set. In the first it is found that in a complete inner product space, the metric half-space topology is the same as one defined in terms of linear functionals on the space. In the second it is proven that in Rn the metric half-space topology is the same as the usual metric topology. In the third theorem it is shown that in a certain sense the nature of the metric halfspace topology generated by a norm on the space determines whether the norm is quadratic, that is to say, whether or not there exists an inner product on the space with the property that |x|^2=(x,x) for all x in the space.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc131510
Date05 1900
CreatorsDooley, Willis L.
ContributorsBilyeu, Russell Gene, Mohat, John T., 1924-
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatiii, 32 leaves, Text
RightsPublic, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Dooley, Willis L.

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