On the cardinality of Urysohn spaces and weakly $H$-closed spaces

summary:We introduce the cardinal invariant $\theta $-$aL'(X)$, related to $\theta $-$aL(X)$, and show that if $X$ is Urysohn, then $|X|\leq 2^{\theta \text {-}aL'(X)\chi (X)}$. As $\theta $-$aL'(X)\leq aL(X)$, this represents an improvement of the Bella-Cammaroto inequality. \endgraf We also introduce the classes of firmly Urysohn spaces, related to Urysohn spaces, strongly semiregular spaces, related to semiregular spaces, and weakly $H$-closed spaces, related to $H$-closed spaces