Variations on known and recent cardinality bounds

Fortunata Aurora Basile, Maddalena Bonanzinga, Nathan Carlson

Sapirovskii [18] proved that $|X|\le \pi \chi (X{)}^{c(X)\psi (X)}$, for a regular space $X$. We introduce the $\theta$-pseudocharacter of a Urysohn space $X$, denoted by ${\psi }_{\theta }(X)$, and prove that th…