Extensions of Boolean isometries

TL;DR

This paper investigates conditions under which maps between subsets of Boolean domains can be extended to automorphisms, focusing on preservation of Boolean distance in various algebraic contexts.

Contribution

It establishes necessary and sufficient conditions for extending maps to automorphisms in Boolean algebras, especially when they are complete, finite, or Boolean domains.

Findings

Preservation of Boolean distance characterizes extendability in complete Boolean algebras.

Finite and Boolean domain subsets also admit extensions under distance-preserving maps.

The paper provides a unified framework for understanding automorphism extensions in Boolean structures.

Abstract

We study when a map between two subsets of a Boolean domain W can be extended to an automorphism of W. Under many hypotheses, if the underlying Boolean algebra is complete or if the sets are finite or Boolean domains, the necessary and suficient condition is that it preserves the Boolean distance between every couple of points.