Continuous families of properly infinite C*-algebras

TL;DR

This paper investigates conditions under which continuous C*-algebras with properly infinite fibers remain properly infinite when the base space has infinite topological dimension, extending previous results for finite-dimensional spaces.

Contribution

It extends the understanding of proper infiniteness in continuous C*-algebras to cases where the base space has infinite topological dimension.

Findings

Proper infiniteness holds for finite-dimensional base spaces.

Conditions identified for infinite-dimensional base spaces.

Analysis of how topological dimension affects proper infiniteness.

Abstract

Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topolog-ical dimension. We study conditions under which this is still the case if the compact space X has infinite topological dimension.