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Cardinal functions <i>F</i><sub>0</sub>(<i>X</i>) and <i>t</i><sub>0</sub>(X) for <i>H</i>-closed spaces
Abstract
This article extends the results proved by Cammaroto and Kocinac in 1993 by showing that t0(X) = t0(Xs) = t(Xs) = F0(X) = F0(Xs) = F(Xs) 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
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
