# New bounds on the cardinality of n-Hausdorff and n-Urysohn spaces

## TL;DR

This paper introduces new cardinal functions for n-Hausdorff and n-Urysohn spaces, providing bounds on their cardinalities and exploring properties of n-Urysohn n-H-closed spaces.

## Contribution

It defines new cardinal functions extending pseudocharacter concepts and derives bounds on the size of n-Urysohn spaces, advancing the understanding of their structure.

## Key findings

- Bounds on the cardinality of n-Urysohn spaces are established.
- Properties of n-Urysohn n-H-closed spaces are proved.
- New cardinal functions generalize existing concepts in topology.

## Abstract

Two new cardinal functions defined in the class of $n$-Hausdorff and $n$-Urysohn spaces that extend pseudocharacter and closed pseudocharacter respectively are introduced. Through these new functions bounds on the cardinality of $n$-Urysohn spaces that represent variations of known results are given. Also properties of $n$-Urysohn $n$-H-closed spaces are proved.