A property of C_p[0,1]

TL;DR

This paper demonstrates that for any finite-dimensional compact metric space, there exists an open continuous linear surjection from the space of continuous functions on [0,1] to the space of continuous functions on that space, using embeddings related to Hilbert's 13th problem.

Contribution

It establishes a universal property of C_p[0,1] by constructing open linear surjections onto C_p(X) for all finite-dimensional compact metric spaces, leveraging classical embeddings.

Findings

Existence of open continuous linear surjections from C_p[0,1] to C_p(X)

Use of Kolmogorov and Sternfeld embeddings in the proof

Connection to Hilbert's 13th problem

Abstract

We prove that for every finite dimensional compact metric space $X$ there is an open continuous linear surjection from $C_p[0,1]$ onto $C_p(X)$. The proof makes use of embeddings introduced by Kolmogorov and Sternfeld in connection with Hilbert's 13th problem.