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A Characterization of Continuity Revisited


Gámez Merino, José Luis and Muñoz-Fernández, Gustavo A. and Seoane Sepúlveda, Juan Benigno (2011) A Characterization of Continuity Revisited. American Mathematical Monthly, 118 (2). pp. 167-170. ISSN 0002-9890

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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 2(c)-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.

Item Type:Article
Subjects:Sciences > Mathematics > Topology
ID Code:16895

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Deposited On:26 Oct 2012 09:01
Last Modified:14 Mar 2016 15:33

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