Span zero continua and the pseudo-arc (Q1174666)

A (metric) continuum is said to be of span zero if each two maps into it have a coincidence if they are defined on a continuum and if they have the same image [\textit{A. Lelek}, Topology Proc. 9, 193--196 (1984; Zbl 0568.54025)]. It is known that continua of span zero are continuous images of the pseudo-arc [\textit{J. F. Davis}, Proc. Am. Math. Soc. 90, 133--138 (1984; Zbl 0538.54026); \textit{L. G. Oversteegen} and \textit{E. D. Tymchatyn}, Fundam. Math. 123, 137--149 (1984; Zbl 0557.54022)]. In the paper under review a method for obtaining maps from the pseudo-arc onto continua of span zero is described in terms of near commutative diagrams of approximating maps in the sense of a reviewer's lemma [Colloq. Math. 10, 39--44 (1963; Zbl 0118.18205)]. A condition assuring preservation of the property of being of span zero under continuous maps is established. The paper ends with fixed point theorems for continua of span zero which generalize theorems by \textit{R. Rosen} (1959) concerning fixed points of multivalued maps on chainable continua.