*Definition [#t018d8ba]
A subspace Y is defined to be countably Aull-pamcompact in a topological space X if for every countable collection U of open subsets of X with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$Y%5csubset%5ccup%20%5cmathcal%7bU%7d$%7d%25.png);, there exists a collection V of open subsets of X with &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$Y%5csubset%5ccup%20%5cmathcal%7bV%7d$%7d%25.png); such that V is a [[partial refinement]] of U and V is [[locally finite]] at each point of Y.
*Remark [#vcbdddc3]
-It is not a property for topological spaces but subspaces.

*Reference [#lf09d3a5]
-S. Kawaguchi, ''Results on relative expandability and relative pseudocompactness'', Kyoto Univ. RIMS Kokyuroku, Vol.1492 (2006) pp.104-119