Some Properties of Metric Spaces

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Description

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 ... continued below

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iii, 40 leaves

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Brazile, Robert P. August 1964.

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  • Brazile, Robert P.

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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.

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iii, 40 leaves

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  • August 1964

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  • June 24, 2015, 9:39 a.m.

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  • Oct. 5, 2016, 4:43 p.m.

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Citations, Rights, Re-Use

Brazile, Robert P. Some Properties of Metric Spaces, thesis, August 1964; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc663798/: accessed January 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .