Regular Points of a Subcartesian Space

TL;DR

This paper investigates the regular part of a subcartesian space, establishing its openness, density, and the local triviality of the tangent bundle restriction, thus enhancing understanding of its geometric structure.

Contribution

It proves that the regular part of a subcartesian space is open, dense, and has a locally trivial tangent bundle, clarifying its geometric properties.

Findings

$S_{reg}$ is open and dense in $S$

The tangent bundle restriction to $S_{reg}$ is locally trivial

Provides foundational properties of the regular part in subcartesian spaces

Abstract

We discuss properties of the regular part $S_{reg}$ of a subcartesian space $S$. We show that $S_{reg}$ is open and dense in $S$ and the restriction to $S_{reg}$ of the tangent bundle of $S$ is locally trivial.