This problem has Hartshorne Height 1.
- Show the complement of is open. If then since the stalk is a direct limit, for s to map to 0 in the stalk means it maps to 0 in some small enough open neighborhood of the point. So the any point in the complement is an interior point.
- One example for not being closed. Take with the usual topology. The for any open set consider the set of real valued functions which are 0 if . Then is