A Characterization of Continuity Revisited



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

Official URL: http://www.ingentaconnect.com/content/maa/amm/2011/00000118/00000002/art00009


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
Deposited On:26 Oct 2012 09:01
Last Modified:25 Nov 2016 12:12

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