*Definition [#b3ceb67c]
A space X is almost &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cmathbb%7bR%7d$%7d%25.png);-paracompact iff every open covering of X of cardinality &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$%5cle%5cmathbb%7bR%7d$%7d%25.png); has an open [[locally finite]] refinement whose union is dense in X. It is equivalent to [[almost $\Aleph$-paracompactness>almost m-paracompact]].

*Reference [#b9b2daf8]
-Cao Ji-Ling, ''Weakly closed multifunctions and paracompactness'', Internat. J. Math and Math. Sci. Vol.16, No.2, pp.345-350 (1993).