Cleavability of Decomposition Spaces

Abstract

Assume that X and Y have the same homotopy type, if X (respectively Y) is cleavable over p, have proved that the decomposition space of Y/g (respectively X/f) is cleavable over p. A result ncerning Arhangel'skii - Teroni's problem is obtained, also some results concerning cleavable ices and (strong) straightenable spaces are obtained. Some open problems related with homotopy a d homology theories are given.