Some Properties of Metric Spaces

• Main Author: Brazile, Robert P.
• Other Authors: Mohat, John T., 1924-
• Format: Others
• Language: English
• Published: North Texas State University 1964
• Subjects: metric spaces; topological spaces
• Online Access: https://digital.library.unt.edu/ark:/67531/metadc663798/

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.