On cardinality bounds for ${\theta }^n$-Urysohn spaces

Abstract

We introduce the class of ${\theta }^n$-Urysohn spaces and the $n$-$\theta$-closure operator. ${\theta }^n$-Urysohn spaces generalize the notion of a Urysohn space. We estabilish bounds on the cardinality of these spaces and cardinality bounds if the space is additionally homogeneous.

14 pages