Some homotopy classification and extension theorems for the class of compositions of acyclic set-valued maps
The presented paper gives an essential advance in the theory of multivalued mappings, in particular in the homotopy classification both of single valued and multivalued mappings and the fixed point theory. The author generalizes the Hopf homotopy classification theorem and also proved an extension theorem for multivalued mappings. The obtained results give us positive answers to some old questions of the theory of multivalued mappings concerning the validity of the Hopf theorem for acyclic multivalued mappings. The main tools rely on the proved theorem (comp. Theorem 2.17 and also 2.11) stating that a perfect surjection with acyclic fibres induces a bijective transformation of the sets of homotopy classes and constituting an extension of the famous Vietoris-Begle mapping theorem.
scientific article; zbMATH DE number 812669