The study of metric spaces is closely related to the study of topology in that the study of metric spaces concerns itself, also, with sets of points and with a limit point concept based on a function which gives a "distance" between two points. In some topological spaces it is possible to define a distance function between points in such a way that a limit point of a set in the topological sense is also a limit point of the same set in a metric sense. In such a case the topological space is "metrizable". The real numbers with its usual topology is an example of a topological space which is metrizable, the distance function being the absolute value of the difference of two real numbers. Chapters II and III of this thesis attempt to classify, to a certain extent, what type of topological space is metrizable. Chapters IV and V deal with several properties of metric spaces and certain functions of metric spaces, respectively.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc663798 |
| Date | 08 1900 |
| Creators | Brazile, Robert P. |
| Contributors | Mohat, John T., 1924-, Copp, George |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 40 leaves, Text |
| Rights | Public, Brazile, Robert P., Copyright, Copyright is held by the author, unless otherwise noted. All rights |
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