$K$-theory of co-existentially closed continua

TL;DR

This paper investigates the K-theory of C*-algebras associated with co-existentially closed continua, revealing the range of possible K-theory values and classifying certain pseudo-solenoids as not co-existentially closed.

Contribution

It characterizes the K-theory of C(X) for co-existentially closed continua and identifies which pseudo-solenoids are not co-existentially closed.

Findings

Determines the possible K-theory values for C(X) when X is co-existentially closed.

Shows that most pseudo-solenoids are not co-existentially closed.

Provides a classification result for pseudo-solenoids based on co-existential closure.

Abstract

We describe the possible values of $K$-theory for $C(X)$ when $X$ is a co-existentially closed continuum. As a consequence we also show that all pseudo-solenoids, except perhaps the universal one, are not co-existentially closed.