Andrei Catalioto

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.

On H-closed and U-closed functions

Abstract In this article, we extend the work on H-closed functions started by Cammaroto, Fedorchuk and Porter in 1998. Also, U-closed functions are introduced and characterized in terms of filters and adherence. The hereditary and productivity properties are examined and developed for both H-closed and U-closed functions.

On minimal Hausdorff and minimal Urysohn functions

In this article, we extend the work on minimal Hausdorff functions initiated by Cammaroto, Fedorchuk and Porter in a 1998 paper. Also, minimal Urysohn functions are introduced and developed. The properties of heredity and productivity are examined and developed for both minimal Hausdorff and minimal Urysohn functions.