Atomic mappings can spoil lightness of open mappings (Q5933601)

\(L\) 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 a continuum \(X\) is arcwise connected, then \(f(X) \in L\). NEWLINENEWLINENEWLINEIn this paper the authors construct in the class \(L\) an uncountable family of non-arcwise connected continua and atomic mappings defined on the continua such that the range spaces are not in \(L\). This gives a negative answer to \textit{W. Makuchowski}'s question [Commentat. Math. Univ. Carol. 35, No. 4, 779-788 (1994; Zbl 0830.54014)]. NEWLINENEWLINENEWLINEA nice continuum \(X\) is presented in Example 2.10. The continuum \(X\) has the properties: (1) \(X\) is not arcwise connected, (2) \(X\) is arclike, (3) each nonconstant open mapping defined on \(X\) is a homeomorphism, and (4) there exists an atomic mapping \(f\) defined on \(X\) such that \(f(X)\) is not in \(L\).