A Characterization of Ptàk Spaces.
If is an infrabarrelled space, it is proved that any subspace , of finite codimension, is infrabarrelled.
Recently Cascales, Kąkol and Saxon showed that in a large class of locally convex spaces (so called class G) every Fréchet-Urysohn space is metrizable. Since there exist (under Martin’s axiom) nonmetrizable separable Fréchet-Urysohn spaces Cp(X) and only metrizable spaces Cp(X) belong to class G, we study another sufficient conditions for Fréchet-Urysohn locally convex spaces to be metrizable.