A note on the continuous self-maps of the ladder system space

TL;DR

This paper characterizes continuous self-maps of the ladder system space K_S, revealing its high nonrigidity and showing that the associated function space C(K_S) lacks the property of having few operators.

Contribution

It provides a partial characterization of continuous self-maps of K_S and demonstrates the nonrigidity and operator properties of C(K_S).

Findings

K_S is highly nonrigid.

C(K_S) does not have few operators.

Partial characterization of self-maps of K_S.

Abstract

We give a partial characterization of the continuous self-maps of the ladder system space K_S. Our results show that K_S is highly nonrigid. We also discuss reasonable notions of "few operators" for spaces C(K) with scattered K and we show that C(K_S) does not have few operators for such notions.