An answer to a question of R. G. Gibson and F. Roush (Q910877)

The author shows that there exists a connected real valued function on [0,1] which is not almost continuous. As a corollary he obtains an answer to a question of \textit{R. G. Gibson} and \textit{F. Roush} [Real Anal. Exch. 11, 254-259 (1986; Zbl 0605.26004), see also \textit{A. M. Bruckner} and \textit{J. Ceder}, Czech. Math. J. 22(97), 435-448 (1972; Zbl 0239.26005)] saying that there exists a connectivity function from [0,1] to itself which is not the uniform limit of a sequence of almost continuous functions.