Mathematica Bohemica, Vol. 144, No. 3, pp. 325-336, 2019
On the cardinality of Urysohn spaces and weakly $H$-closed spaces
Fortunata Aurora Basile, Nathan Carlson
Received March 21, 2018. Published online November 27, 2018.
Abstract: We introduce the cardinal invariant $\theta$-$aL'(X)$, related to $\theta$-$aL(X)$, and show that if $X$ is Urysohn, then $|X|\leq2^{\theta\text-aL'(X)\chi(X)}$. As $\theta$-$aL'(X)\leq aL(X)$, 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.
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Affiliations: Fortunata Aurora Basile, University of Messina, Piazza Pugliatti, 1-98122 Messina, Italy, e-mail: basilef@unime.it; Nathan Carlson, Department of Mathematics, California Lutheran University, 60 W Olsen Rd, Thousand Oaks, CA 91360, California, USA, e-mail: ncarlson@callutheran.edu
