Multi-selectible continua

Joseph Edward McParland, West Virginia University


A particular coexistence of multiple continuous selections (a "multi-selection") within a function space for a non-degenerate metric continuum X is investigated for the hyperspaces 2X and C(X). It is demonstrated that (i) multi-selections do not exist for 2X and that (ii) the existence of a multi-selection for C(X) is equivalent to X being a dendrite.