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Mathematical Analysis Fundamentals by Agamirza Bashirov

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Chapter 5

Continuity

Abstract

Chapter 5 includes a first discussion of continuous functions. It starts with the definition of continuous functions in metric spaces and its discussion. Examples of a construction of different discontinuous functions are given. The limit concept for a function is defined and it is related to continuity. A special attention is giving to discontinuity points of real-valued functions of real variable. Continuous functions on compact and connected metric spaces are studied. Oscillation of a function is defined and related to continuity. The chapter ends with discussion of continuity for functions with values in finite dimensional Euclidean spaces.

Keywords

Continuity; discontinuity; limit of a function; Intermediate value ...

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