A New Proof of the Weyl-von Neumann-Berg Theorem

TL;DR

This paper presents a novel proof of the Weyl-von Neumann-Berg theorem, enhancing previous proofs by leveraging the continuous image property of compact sets, thus providing a more elegant approach.

Contribution

The paper introduces a new proof technique for the Weyl-von Neumann-Berg theorem that simplifies and improves upon Halmos' 1972 proof.

Findings

The new proof is more concise and elegant.

It demonstrates that every compact set in the complex plane is a continuous image of a compact set in the real line.

The approach offers a deeper understanding of the theorem's underlying structure.

Abstract

We give a new proof of the Weyl-von Neumann-Berg theorem. Our proof improves Halmos' proof in 1972 by observing the fact that every compact set in the complex plane is the continuous image of a compact set in the real line.