IJPAM: Volume 79, No. 1 (2012)
Departamento de Álgebra y Análisis Matemático
Universidad de Almerıa
04120, Almerıa, SPAIN
Departamento de Análisis Matemático
Universidad de Granada
18071, Granada, SPAIN
Abstract. In this paper we prove that the discontinuity set of any bijective function from to is infinite. We then proceed to give a gallery of examples which shows that this is the best we can expect, and that it is possible that any intermediate case exists.
We conclude with an example of a (nowhere continuous) bijective function which exhibits a dense graph in the rectangle
Received: April 19, 2012
AMS Subject Classification: 26A06, 26A09
Key Words and Phrases: discontinuity set, fixed point
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395