# Corson reflections

## TL;DR

This paper establishes a reflection principle for Corson compacta in a specific set-theoretic model, linking Corson compactness to continuous images of weight , using Gelfand--Naimark duality and star-algebras.

## Contribution

It introduces a new reflection principle for Corson compacta in a forcing extension involving a supercompact cardinal, connecting topological and algebraic perspectives.

## Key findings

- Corson compacta reflect to their  continuous images in the model
- The reflection principle holds after Levy-collapsing a supercompact cardinal
- Results are expressed via Gelfand--Naimark duality and star-algebras

## Abstract

A reflection principle for Corson compacta holds in the forcing extension obtained by Levy-collapsing a supercompact cardinal to~$\aleph_2$. In this model, a compact Hausdorff space is Corson if and only if all of its continuous images of weight~$\aleph_1$ are Corson compact. We use the Gelfand--Naimark duality, and our results are stated in terms of unital abelian \cstar-algebras.