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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.
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Document Type: Short Communication

Publication date: 2011-02-01

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