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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
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.118.02.167
Page Count: 4
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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.
Copyright the Mathematical Association of America 2011