microcompact

Definition

A topological space X is called microcompact if for every point x in X and every neighborhood V of x, there is a compact Hausdorff neighborhood U of x which is included in V.

Reference

• Mathieu Baillif and Alexandre Gabard, Manifolds: Hausdorffness versus homogeneity, Proc. Amer. Math. Soc. 136 (2008) 1105-1111.