retrocompact

Definition

Let X be a topological space.
A subset C is called retrocompact if for every quasi-compact (i.e. compact but not necessarily Hausdorff) open set U, the intersection of U and C is quasi-compact.

Reference

Ulrich Gortz and Torsten Wedhorn, Algebraic geometry I: schemes with examples and exercises, Vieweg Teubner Verlag, 2010.