Cardinal functions F0(X) and t0(X) for H-closed spaces

Abstract

This article extends the results proved by Cammaroto and Kocinac in 1993 by showing that t₀(X) = t₀(X_s) = t(X_s) = F₀(X) = F₀(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, ,t₀, F and F₀ in the context of H-closed and Urysohn spaces. Also, an H-closed space H is constructed for which F₀(H) < t₀(H). Two questions posed by Cammaroto and Kocinac about H-closed spaces are completely answered.

Keywords: Closure, ϑ -closure, free sequence, ϑ -free sequence, t(X), t₀(X), F(X), F₀(X), compact spaces, H-closed spaces, Urysohn spaces

Quaestiones Mathematicae,/i> 37(2014), 309-320