A Study of Functions on Metric Spaces
Richard S. Brice
Abstract
Open-access reader
Richard S. Brice
Abstract
Open-access reader
This thesis describes various forms of metric spaces and establishes some of the properties of functions defined on metric spaces. No attempt is made in this paper to examine a particular type of function in detail. Instead, some of properties of several kinds of functions will be observed as the functions are defined on various forms of metric spaces such as connected spaces, compact spaces, complete spaces, etc.
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This thesis describes various forms of metric spaces and establishes some of the properties of functions defined on metric spaces. No attempt is made in this paper to examine a particular type of function in detail. Instead, some of properties of several kinds of functions will be observed as the functions are defined on various forms of metric spaces such as connected spaces, compact spaces, complete spaces, etc.
Key concepts: Metric space, Mathematics, Metric map, Uniform continuity, Pure mathematics, Fréchet space, Convex metric space, Function space