On functors of finite degree and \(\kappa\)-metrizable bicompact spaces (Q2773627)

The author introduces the notion of strictly epimorphic covariant functor acting in the category Comp. The main result is given by the following NEWLINENEWLINENEWLINETheorem: If \(F\), \(G\) are semi-normal strictly epimorphic functors, \(X\), \(Y\) belong to the class \(HC\) of the with respect to the character uniform \(\kappa\)-metrizable bicompact spaces of non-countable weight, and the spaces \(F_m(X)\), \(G_n(Y)\) are homeomorphic to each other then the spaces \(F_{m-1}(X)\), \(G_{n-1}(Y)\) are also homeomorphic to each other \((m,n\geq 3)\). NEWLINENEWLINENEWLINEThe functor of complete \(k\)-linked systems \(N^k\) \((k\geq 2)\) as well as the functors exp, \(\lambda\), and \(P\) satisfy the conditions of the theorem. For all above-mentioned functors, the author obtains corollaries asserting that spaces of the form \(F_m(X)\) and \(F_n(Y)\) are not mutually homeomorphic for almost all \(X,Y\in HC\).