On cardinality bounds for θ^n-Urysohn spaces

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.