Cardinal functions F_θ(X) and t_θ(X) for H-closed spaces

Abstract

This article extends the results proved by Cammaroto and Kočinac in 1993 by showing that t_θ(X) = t_θ(X_s) = t(X_s) = F_θ(X) = F_θ(X_s) = F(X_s) for every H-closed and Urysohn space. Examples are developed to study all of the relationships among the cardinal functions t, t_θ, F and F_θ in the context of H-closed and Urysohn spaces. Also, an H-closed space H is constructed for which F_θ(H) < t_θ(H). Two questions posed by Cammaroto and Kočinac about H-closed spaces are completely answered.