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

Abstract

We introduce the cardinal invariant θ-aL ′ (X), related to θ-aL(X), and show that if X is Urysohn, then |X| 2 θ-aL ′ (X)χ(X). As θ-aL ′ (X) aL(X), this represents an improvement of the Bella-Cammaroto inequality. 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.