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.