Generalization of the Grothendieck's theorem

In this paper, we obtain a generalization of Grothendieck's theorem for the space continuous mappings Cλ,μ(X,Y) where Y is complete uniform with uniformity μ endowed topology convergence on family λ subsets X. A new topological game defined - Asanov-Velichko game, which makes it possible to single out class spaces Grothendieck type. The developed technique used generalize set-open topology.