°Informally, a
set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.
°A
set which can be described as an (arbitrary)
union of
open balls. Equivalently, a set such that for every
point in it, there is an open ball centered at that point, such that that open ball is contained by the set.