A dimensional property of Cartesian product

TL;DR

This paper proves that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is not hereditarily infinite dimensional, using algebraic topology, revealing a surprising dimensional property.

Contribution

It introduces a novel dimensional property of Cartesian products and employs algebraic topology in a new way to prove this specific non-hereditary infinite dimensionality result.

Findings

The Cartesian product of three hereditarily infinite dimensional spaces is not hereditarily infinite dimensional.

The proof relies on algebraic topology techniques.

This result was previously unknown and is surprising in the context of infinite dimensional topology.

Abstract

We show that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is never hereditarily infinite dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.