*Definition [#vb6d2cc7]
-A space X is monotonically paracompact if one can assign to each open cover U a star-renement μ(U) such that V refines U implies μ(V) refines μ(U).

*Reference [#i49a0f6d]
-Gruenhage, Gary, ''Metrizable spaces and generalizations.'', Hušek, Miroslav (ed.) et al., Recent progress in general topology II. Based on the Prague topological symposium, Prague, Czech Republic, August 19-25, 2001. Amsterdam: Elsevier. 201-225 (2002).