A counterexample regarding an equivalence relation on a product space

TL;DR

This paper provides a counterexample to a specific conjecture about Borel equivalence relations on product spaces, challenging previous assumptions in the field.

Contribution

It introduces a counterexample that disproves a conjecture about the properties of Borel equivalence relations on product spaces.

Findings

Counterexample invalidates the conjecture

Clarifies limitations of Borel equivalence relations

Advances understanding of product space structures

Abstract

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.