##  [Vietoris Topology](/index.php/vietoris-topology) 

  ##  [Vietoris Topology](https://puremath.quantumdictionary.io/vietoris-topology-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A topology on a hyperspace of closed (or compact) subsets of a topological space X generated by hitting and containment conditions with open sets: typical subbasis elements are {F: F⊂U} (upper/hitting) and {F: F∩U≠∅} (lower/hitting), and the full Vietoris topology is generated by both types.