Short proof of a theorem of Juhasz

TL;DR

This paper presents a straightforward proof of an enhanced version of Arhangel'skii's Theorem, which also provides a refined result related to Juhász's theorem, advancing understanding in topological space properties.

Contribution

It introduces a simplified proof technique that strengthens Arhangel'skii's Theorem and refines Juhász's related result, offering new insights in topology.

Findings

Simplified proof of an enhanced Arhangel'skii's Theorem

Refinement of Juhász's theorem

Improved understanding of topological space properties

Abstract

We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.