Algebraic reflexivity of diameter-preserving linear bijections between $C(X)$-spaces

TL;DR

This paper proves that all diameter-preserving linear bijections between spaces of continuous functions on first countable compact Hausdorff spaces are algebraically reflexive, revealing a structural property of such transformations.

Contribution

It establishes the algebraic reflexivity of diameter-preserving linear bijections between $C(X)$-spaces for first countable compact Hausdorff spaces, a novel structural insight.

Findings

Diameter-preserving linear bijections are algebraically reflexive.

The result applies specifically to $C(X)$-spaces with first countable compact Hausdorff spaces.

Provides a new understanding of the structure of such bijections.

Abstract

We prove that if $X$ and $Y$ are first countable compact Hausdorff spaces, then the set of all diameter-preserving linear bijections from $C(X)$ to $C(Y)$ is algebraically reflexive.