Ri-sets, pseudo-contractibility and weak contractibility on hyperspaces of continua

Abstract

In this paper we discuss the notions of pseudo-contractibility and weak contractibility on hyperspaces of (Hausdorff) continua. Also we prove that if a continuum X contains an R i-set then it is not pseudocontractible. As a consequence we have that the existence of an R i-set in a continuum X implies non(pseudo)-contractibility of some hyperspaces.