# Open embeddings and pseudoflat epimorphisms

## TL;DR

This paper characterizes open embeddings of Stein spaces and smooth manifolds through flatness conditions on their function algebra homomorphisms, providing algebraic criteria for geometric embeddings.

## Contribution

It introduces a new algebraic characterization of open embeddings using flatness conditions on homomorphisms of function algebras.

## Key findings

- Open embeddings correspond to flat homomorphisms of function algebras.
- Provides algebraic criteria for geometric embedding properties.
- Links geometric embedding concepts with algebraic flatness conditions.

## Abstract

We characterize open embeddings of Stein spaces and of $C^\infty$-manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras.