A Characterization of Continuity Revisited
Abstract: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
Publication date: February 1, 2011
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- American Mathematical Monthly publishes articles, notes, and other features about mathematics and the profession. AMM readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels.
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