On some properties on span (Q1099431)

The concept of span was introduced by \textit{A. Lelek} [Fundam. Math. 55, 199-214 (1964; Zbl 0142.398)]. It is an open problem whether each span zero continuum is chainable. \textit{I. Rosenholtz} proved that each open map between continua preserves chainability [Proc. Am. Math. Soc. 42, 258-264 (1974; Zbl 0276.54033)]. We show that each open map between continua preserves span zero, which gives an affirmative answer to a question of \textit{E. Duda} [\textit{W. Lewis}, Continuum theory problems, problem 162, Topology Proc. 8, 361-394 (1983)]. Some other properties of continua concerning span are discussed.