Let X, Y be two compacta with Sh(X) = Sh (Y). Then, the spaces of components of X, Y are homeomorphic. This does not happen, in general, when X, Y are quasi-equivalent. In this paper we give a sufficient condition for the existence of a homeomorphism between the spaces of components of two quasi-equivalent compacta X, Y which maps each component in a quasi-equivalent component.
@article{urn:eudml:doc:39262, title = {Quasi-equivalence of compacta and spaces of components.}, journal = {Collectanea Mathematica}, volume = {31}, year = {1980}, pages = {3-10}, zbl = {0447.54037}, mrnumber = {MR0601472}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39262} }
Rodríguez Sanjurjo, José M. Quasi-equivalence of compacta and spaces of components.. Collectanea Mathematica, Tome 31 (1980) pp. 3-10. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39262/