##  [Manifold](/manifold) 

  ##  [Manifold](https://mathlogic.quantumdictionary.io/manifold-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A topological space that is locally homeomorphic to Euclidean space of a fixed dimension, equipped when needed with additional structure (smooth, differentiable, Riemannian) to support calculus and geometric constructions.

 

 

 

 

 





 

 



 ##  [Manifold](https://puremath.quantumdictionary.io/manifold-1) 

  

 [![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 topological space that is locally homeomorphic to Euclidean space R^n; often equipped with extra structure (smooth, differentiable, analytic, or topological) specified via atlases of coordinate charts and transition maps of a given regularity class.