monotonically paracompact

Definition

• 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

• 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).