##  [Local Cut Point](/local-cut-point) 

  ##  [Local Cut Point](https://puremath.quantumdictionary.io/local-cut-point-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 local cut point is a point in a topological space that admits a neighborhood whose removal (i.e., deleting the point from that neighborhood) disconnects that neighborhood into two or more components; it captures separation at small scales rather than removal from the whole space.