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

TL;DR

This paper introduces $ heta^{n}$-Urysohn spaces and the $n$-$ heta$-closure operator, establishing bounds on their cardinalities, especially for homogeneous spaces, thus generalizing classical Urysohn space concepts.

Contribution

It defines a new class of spaces and provides cardinality bounds, extending the understanding of Urysohn spaces and their homogeneous variants.

Findings

Established cardinality bounds for $ heta^{n}$-Urysohn spaces

Derived bounds for homogeneous $ heta^{n}$-Urysohn spaces

Generalized classical Urysohn space results

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.