A Characterization of Continuity Revisited

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It is well known that a function f : R → R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2c-dimensional linear spaces of nowhere continuous functions that (except for the zero function) transform compact sets into compact sets and connected sets into connected sets respectively.

Document Type: Short Communication

DOI: http://dx.doi.org/10.4169/amer.math.monthly.118.02.167

Publication date: February 1, 2011

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