Velichko's notions close to sequentially separability and their hereditary variants in Cₚ-theory

A space X is sequentially separable if there is a countable S X such that every point of X is the limit of a sequence of points from S. In 2004, N. V. Velichko defined and investigated concepts close to sequentially separable: -separability and F-separability. The aim of this paper is to study -separability and F-separability (and their hereditary variants) of the space Cₚ (X) of all real-valued continuous functions, defined on a Tychonoff space X, endowed with the pointwise convergence topology. In particular, we proved that -separability coincides with sequential separability. Hereditary variants (hereditarily -separablity and hereditarily F-separablity) coincides with Frechet-Urysohn property in the class of cosmic spaces.