##  [Boundary at Infinity](/boundary-infinity) 

  ##  [Boundary at Infinity](https://puremath.quantumdictionary.io/boundary-infinity-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The boundary at infinity of a noncompact metric or geometric space is an adjoined set of ideal points representing asymptotic equivalence classes of divergent sequences, geodesic rays, or horofunction limits; it provides a compactification capturing directions or limit behaviours at large scale determined by a chosen equivalence relation.