On g-contractibility of continua

A continuum X is g-contractible provided that there exists an onto map f:X→X such that f is homotopic to a constant map. Thus, g-contractibility is a natural generalization of contractibility. In this paper we present properties related to the g-contractibility of products and symmetric products of continua.Furthermore, we show an uncountable family of pairwise non-homeomorphic, uniformly pathwise connected, non-g-contractible, planar dendroids such that their hyperspaces of subcontinua are not g-contractible either.