Cardinal functions Fθ(X) and tθ(X) for H-closed spaces

Abstract

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