Gámez-Merino, José L. and Muñoz-Fernández, Gustavo Adolfo and Seoane-Sepúlveda, Juan Benigno (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
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 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 |
| References: | R. M. Aron, V. I. Gurariy, and J. B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on R , Proc. Amer. Math. Soc. 133 (2004) 795–803. oi:10.1090/S0002–9939-04–07533-1 J. L. Gámez-Merino, G. A. Mu~noz-Fernández, V. M. Sánchez, and J. B. Seoane-Sepúlveda, Sierpiński-Zygmund functions and other problems on lineability, Proc. Amer. Math. Soc. 138 (2010) 3863–3876. doi:10.1090/50002–9939-2010–10420-3 D. J. Velleman, Characterizing continuity, Amer. Math. Monthly 104 (1997) 318–322. doi:10.2307/2974580 |
| Deposited On: | 26 Oct 2012 11:01 |
| Last Modified: | 26 Oct 2012 11:01 |
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