##  [Isotopy Extension Theorem](/isotopy-extension-theorem) 

  ##  [Isotopy Extension Theorem](https://puremath.quantumdictionary.io/isotopy-extension-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A result in geometric topology that, under appropriate regularity and compactness hypotheses, any isotopy of a subspace or submanifold inside a manifold extends to an ambient isotopy of the whole manifold; equivalently, a deformation of the inclusion can be realized by a deformation of the ambient identity map supported in a neighborhood of the subspace.