core compact

Definition

• 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

• For Hausdorff spaces, core compactness coincides with local compactness.

Reference

• 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).