A concrete co-existential map that is not confluent

We give a concrete example of a co-existential map between continua that is not confluent.

💡 Research Summary

The paper addresses a subtle but important distinction between two notions of maps between continua: co‑existential maps, which arise from model‑theoretic considerations and preserve existential structure via ultrafilters, and confluent maps, a classical topological concept that requires the pre‑image of every connected closed set to remain connected. While it has often been tacitly assumed that co‑existentiality might imply confluence, no explicit counterexample had been presented. The author constructs a concrete example that settles this question definitively.

First, the author recalls the definitions. A map f : X → Y between compact connected metric spaces (continua) is co‑existential if for every ultrafilter 𝒰 on X, the image filter f