##  [Compact-Open Topology](/compact-open-topology) 

  ##  [Compact-Open Topology](https://puremath.quantumdictionary.io/compact-open-topology-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A topology on the space C(X,Y) of continuous maps from X to Y generated by subbasic sets of the form [K,U]={f∈C(X,Y):f(K)⊂U}, where K⊂X is compact and U⊂Y is open; it encodes control of maps on compact subsets of the domain.