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Systems of Continuos Functions

Part of the Universitext book series (UTX)

Abstract

Topological spaces were introduced in the first place because they are the natural habitat for continuous functions.

Given two topological spaces X and Y , the number of continuous functions from X to Y can vary greatly, depending on the topologies involved: everything is possible from “all functions are continuous” to “only the constants are continuous.” In this chapter, we are interested in continuous functions from topological spaces into R or C. On a metric space, the metric itself easily provides a plentiful supply of such functions. But can anything meaningful be said in the absence of a metric?

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Copyright information

© Springer Science+Business Media, Inc. 2005

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