gn.general topology - Name for a kind of topological property?

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 $Vsubset U$




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.

CLARIFICATION: My main question is really: is there existing terminology for such
a property?

I will, however be happy to consider suggestions on the secondary question: if not, then what should I call it?