Irreducible mapping and the lightness of open mappings (Q2782156)

\(L\) denotes the class of all continua \(X\) such that each nonconstant open mapping defined on \(X\) is light. It is known that if \(f\) is an atomic mapping and \(X \in\) \(L\) then \(f(X)\) need not to be in \(L\) [\textit{J. J. Charatonik} and \textit{P. Pyrih}, Tsukuba J. Math. 24, No. 1, 157-169 (2000; Zbl 0979.54033)] but if a continuum \(X\) is arcwise connected, then \(f(X) \in \) \(L\). NEWLINENEWLINENEWLINEThe authors show an example of an arcwise connected continuum \(X\) belonging to \(L\) and an irreducible mapping \(f\) defined on \(X\) such that \(f(X)\) is not in \(L\).