Monotone Retracts and Some Characterizations of Dendrites

G. R. Gordh Jr.
Lewis Lum, University of Portland


Let M be a metric continuum containing a fixed point p. The following conditions are shown to be equivalent. (i) M is a dendrite. (ii) Each subcontinuum of M is a monotone retract of M. (iii) M is arcwise connected and each subcontinuum of M containing p is a monotone retract of M.