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