Pseudo-homotopies between maps on g-growth hyperspaces of continua

Abstract

. We introduce the concept of g-growth hyperspace: if X is a continuum, then a non-empty subset H of 2 X is a g-growth hyperspace of X provided that if A is a subcontinuum of 2 X and A∩H (cid:54) = ∅ , then (cid:83) A ∈ H . We study pseudo-homotopies between maps of hyperspaces of continua. As a consequence, we show that pseudo-contractibility and contractibility are equivalent in g-growth hyperspaces.