e-compact

Definition

Lambrinos defined a subset B of a space X to be bounded iff every open cover of X contains a finite subcollection which covers B. Hechler defined a space X to be e-compact with respect to D iff D is a bounded dense subset of X.
X is called e-compact if there exists such a subset D.

Reference

• T. R. Hamlett and Dragan Jankovic, On Weaker Forms of Paracompactness, Countable Compactness, and Lindelöfness, Annals of the New York Academy of Sciences Volume 728, General Topology and Applications pages 41–49, November 1994.
• Lambrino, A topological notion of boundedness, Manuscripta Math. 10, pp.289-296 (1973).
• S. H. Hechler, On a notion of weak compactness in non-regular spaces, Studies in Topology, N. M. Stavrakas and K. R. Allen, Eds. Academic Press, New York, 2, pp.15-237 (1975).