Karchevska L. Topological properties of weakly normal monads

The dissertation is devoted to investigation of properties of weakly normal functors and monads which they generate. In particular, we investigate openness and bicommutativity of the functors of k-nonexpanding functionals; we study geometric properties of monads of semiadditive and positively homogeneous functionals; we investigate the conditions under which the multiplication maps for monads O, OH and OS are trivial fibrations with fibers homeomorphic to the Hilbert or Tychonov cube; we study the properties of the Chigogidze extension of a functor in the category Comp onto category Tych; we prove that the Hartman - Mycielski functor cannot be completed to a monad.