Countable products of spaces of finite sets

TL;DR

This paper classifies the Banach spaces of continuous functions on countable products of compact spaces of finite subsets, providing a comprehensive topological and functional analysis.

Contribution

It offers a complete classification of Banach spaces of continuous functions on these products and a partial topological classification, advancing understanding of their structure.

Findings

Complete classification of Banach spaces of continuous functions

Partial topological classification of the spaces

Insights into the structure of countable products of finite set spaces

Abstract

We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.