Topological vector spaces and function spaces which are κ-Fréchet–Urysohn and have open countable tightness

We characterize topological vector spaces (tvs) which are κ κ -Fréchet–Urysohn or have open countable tightness. It is shown that an infinite-dimensional feral locally convex space is not κ κ -Fréchet–Urysohn. It is proved that the product of a metrizable tvs and a tvs with open countable tightness also has open countable tightness. Let Y be a non-trivial metrizable abelian group, I I be an ideal of compact subsets of a topological space X . Denote by CI(X,Y) C I ( X , Y ) and by CI^*(X,Y) C I ∗ ( X , Y ) the space C ( X , Y ) of all continuous functions and the space C^*(X,Y) C ∗ ( X , Y ) of all continuous functions with relatively compact image endowed with the topology defined by the ideal I I . Generalizing results of M. Sakai and the author it is shown that if X is a strongly (resp., strongly^* strongly ∗ ) YI Y I -Tychonoff space, then (1) CI(X,Y) C I ( X , Y ) (resp., CI^*(X,Y) C I ∗ ( X , Y ) ) has open countable tightness iff every I I -moving off family K⊆ I K ⊆</