What should I call a property (P) of (open) subspaces of a space $X$ such that:

1.  If  $U$  satisfies (P), then so does every open subset $V\subset U$

2.  If "{"$U_i$"}" is a pairwise disjoint collection of sets satisfying (P), then 
$\bigcup_i U_i$ satisfies (P).  (Unable to make braces?)


My understanding is that if (P) satisfies condition 1, then (P) is called a
hereditary property.