Grispolakis, J.; Tymchatyn, E. D. On a characterization of \(W\)-sets and the dimension of hyperspaces. (English) Zbl 0618.54010 Proc. Am. Math. Soc. 100, 557-563 (1987). A subcontinuum \(A\) of a continuum \(X\) is a \(W\)-set if for each mapping \(f\colon Y \twoheadrightarrow X\) of an arbitrary continuum \(Y\) onto \(X\) there is a continuum in \(Y\) which is mapped by \(f\) onto \(A\). We characterize \(W\)-sets in terms of accessibility by small continua. We localize several known results on continua all of whose subcontinua are \(W\)-sets. Finally, we extend a result of J. T. Rogers by proving that if \(X\) is an atriodic continuum whose first Čech cohomology group is finitely generated then the hyperspace \(C(X)\) of subcontinua of \(X\) is two dimensional. Reviewer: J. Grispolakis Cited in 1 Document MSC: 54B20 Hyperspaces in general topology 54F15 Continua and generalizations 54C10 Special maps on topological spaces (open, closed, perfect, etc.) Keywords:weakly confluent mappings; dimension of hyperspaces of subcontinua; W-sets; atriodic continuum; first Čech cohomology group; finitely generated PDFBibTeX XMLCite \textit{J. Grispolakis} and \textit{E. D. Tymchatyn}, Proc. Am. Math. Soc. 100, 557--563 (1987; Zbl 0618.54010) Full Text: DOI