CONTINUOUS FUNCTION IN A COMPACT METRIC SPACE
Abstract
ABSTRACT
As the set of real numbers is the space on which we are operating, it is important that we have a clear idea of the essential properties of this set. But the theory of mapping on the real and complex numbers is very naturally dependent on the theory of sequences, which are mapping onto the natural numbers. Therefore, we introduce the properties of metric space and the real numbers. It could be said that the basic idea of real analysis is the study of the limit concept. We then consider real mappings defined on R or on an interval, and for such mapping we develop the theory of limits and a precise notion of continuity.
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