Shape classification of (projective m-space)-like continua

AbstractThe Mardešić-Segal approach to shape classification of M-like continua (M a compact metric ANR) is reformulated in an algebraic setting. A functor Sh from the category of semigroups to the category of sets is defined which, when applied to [M, M], the semigroup of homotopy classes maps of M into itself, yields the shape classification of M-like continua. The shape classification of all (real projective m-space)-like continua is completely solved