*Definition [#r6049102]
Let X be a topological space, A a subset of X.
We say A is ''parabounded'' if X is [[<X-A>-paracompact>I-paracompact (paracompact modulo I)]] (see [[ideal (family of subsets)]] for notation <X-A>).
X is called ''e-paracompact with respect to A'' if A is a dense parabounded set.
X is called ''e-paracompact'' if there exists such a subset A.

*Reference [#z31b1064]
-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&#8211;49, November 1994.