*Definition [#bc121ee4]
A topological space is said to be quasi-paracompact iff every open cover has a [[locally finite]] [[shrinking]].
*Property [#i175ac93]
The following are equivalent for a space T:
++T is quasi-paracompact;
++T is a T_4 space and each open cover has an open [[locally finite]] refinement.
++For every open cover {U_i}, there exists an open [[locally finite]] cover {W_j} such that {cl(W_j)} refines {U_i}.
*Reference [#ha1b7cfc]
G. Richter and A. Vauth, ''Fibrewise sobriety (from Categorical Structures and their Applications)'', Proc. North-East Euro. Seminar, pp.265-284, World Scientific Publishing Co. Pte. Ltd (2004).