An open set is a set for which every point in the set has a neighborhood lying in the set. An open set is the complement of a closed set and. An open interval is an example of an open set.

Let S be a subset of a metric space. Then the set S is open if every point in S has a neighborhood lying in the set. An open set of radius r and center x_0 is the set of all points x such that left bracketing bar x - x_0 right bracketing bar

ball | Borel set | closed set | empty set | neighborhood | open ball | open disk | open interval | open neighborhood

college level