IJPAM: Volume 53, No. 4 (2009)

ORBITS AND CONTINUITY OF
CERTAIN CLASS OF FUNCTIONS

Kandasamy Muthuvel
Department of Mathematics
University of Wisconsin - Oshkosh
Oshkosh, Wisconsin, 54901-8601, USA
e-mail: muthuvel@uwosh.edu


Abstract.In this paper, we prove that if $g$ is a continuous function that is nonconstant on every nonempty open interval, $f$ is a Darboux function with the dense mapping property, and $g\subseteq \cup _{n\in N}f^{n}$, then the set of all discontinuity points of $f$ is nowhere dense. Among other things, we prove that in the above statement if we replace ``$f$ is a Darboux function with the dense mapping property'' by ``$f$ is a connectivity function without a fixed point'', then $f$ is continuous everywhere.

Received: May 23, 2009

AMS Subject Classification: 26A15, 26A18, 54C30

Key Words and Phrases: connectivity function, quasicontinuous function, Darboux function, dense mapping property, second category

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 4