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1 Distance J Muscat 1. Metric Spaces Joseph Muscat 2003. (Last revised May 2009). (A revised and expanded version of these notes are now published by Springer.). 1 Distance A Metric space can be thought of as a very basic space having a geometry, with only a few axioms. Metric Spaces are generalizations of the real line, in which some of the theorems that hold for R remain valid. Some of the main results in real analysis are (i) Cauchy sequences converge, (ii) for continuous functions f (limn xn ) = limn f (xn ), (iii) continuous real functions are bounded on intervals of type [a, b] and satisfy the intermediate value theorem, etc.

1 Distance J Muscat 1 Metric Spaces Joseph Muscat2003 (Last revised May 2009) (A revised and expanded version of these notes are now published by

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  Space, Metrics, Metric spaces

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