hypocompact

Definition

A topological space is called hypocompact if every cover has a star-finite open refinement.

Remark

• It is also called starparacompact.
• It is also called strongly paracompact.

Reference

• K. Morita, Star-finite coverings and the star-finite property, Math. Japon. I (1948), 60―69.
• S. T. Hu, Cohomology and deformation retracts, Proc. London Math. Soc. 55 (1949), 577-579.
• Lynn Arthur Steen and J. Arthur Seebach, Jr. Counterexamples in Topology, Dover.