Surjective submersion of subcartesian spaces

TL;DR

This paper introduces the concept of submersion in subcartesian differential spaces, extending the classical notion from smooth manifolds and establishing foundational properties for this broader category.

Contribution

It defines submersions in subcartesian spaces and proves their key properties, bridging the gap between manifold theory and more general differential spaces.

Findings

Submersions in subcartesian spaces share properties with those in smooth manifolds.

The paper establishes foundational results for submersion theory in generalized differential spaces.

Abstract

We define the notion of a submersion of subcartesian differential spaces and prove some of its properties, which are analogous to those of a submersion in the category of smooth manifolds and smooth mappings.