A factorization theorem for the cohomological dimensions of mappings (Q1179644)

The possibility is shown of factorizing the perfect mappings of Lindelöf spaces with respect to the weight and to the system of generalized cohomological dimensions of morphisms (which are defined by quadrangular commutative diagrams). In [the author, Russ. Math. Surv. 39, No. 5, 125-153 (1984); translation from Usp. Math. Nauk 39, No. 5(239), 107-130 (1984; Zbl 0588.54034) and Russ. Math. Surv. 36, No. 3, 175-209 (1981); translation from Usp. Mat. Nauk 36, No. 3(219), 147-175 (1981; Zbl 0477.54021)] an analogous result has been obtained for bicompact spaces only. (Passing from bicompact spaces to Lindelöf spaces involves additional difficulties due to the nonperfectness of the maps specifying the morphisms.) The theorem proved in this paper implies the factorization theorem for all cohomological dimensions. In the final part of the paper we formulate a factorization theorem for the morphisms (which are now defined by triangular commutative diagrams) of perfect maps of paracompact spaces, and an extension, to the case of maps, of the Gurevich-Sklyarenko theorem on the bicompactification of the same weight and dimension as those of the space being bicompactified.