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A Characterization of Continuity Revisited

José L. Gámez-Merino, Gustavo A. Muñoz-Fernández and Juan B. Seoane-Sepúlveda
The American Mathematical Monthly
Vol. 118, No. 2 (February 2011), pp. 167-170
DOI: 10.4169/amer.math.monthly.118.02.167
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.118.02.167
Page Count: 4
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A Characterization of Continuity Revisited
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Abstract

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.

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