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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc131510 |
| Date | 05 1900 |
| Creators | Dooley, Willis L. |
| Contributors | Bilyeu, Russell Gene, Mohat, John T., 1924- |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 32 leaves, Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Dooley, Willis L. |
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