##  [Smooth Boundary](/smooth-boundary) 

  ##  [Smooth Boundary](https://puremath.quantumdictionary.io/smooth-boundary-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A boundary that is infinitely differentiable (C∞) at every point so that local charts admit C∞ transition maps and tangent and normal fields are smooth across the boundary.