Abstract

We study properties of the infimal topology τinf which is the infimum of the family of all topologies of uniform convergence defined on the set C(X, Y) of continuous maps into a metrizable space Y. One of the main results of the research consists in obtaining necessary and sufficient condition for the topology τinf to have the Frechet–Urysohn property. We also establish necessary and sufficient conditions for coincidence of the topology τinf and a topology of uniform convergence τμ (“attaining” the infimum). We prove that for this coincidence it is sufficient for the topology τinf to satisfy the first axiom of countability.

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