*Definition [#w71454c3]
-A topological space X is called core compact if every open neighbourhood V of a point x of X contains an open neighbourhood U of x with the property that every open cover of V has a finite subcover of U.


*Remark [#c983eae5]
-For Hausdorff spaces, core compactness coincides with local compactness.

*Reference [#j6e2dde9]
-Escardo, Martín , Lawson, Jimmie and Simpson, Alex, ''Comparing Cartesian closed categories of (core) compactly generated spaces.''[J] Topology Appl. 143, No. 1-3, 105-145 (2004).