Wikipedia lists eleven intervals, which I've made pages for. Here they are, along with their pages and equivalent one-dimensional manifolds. I haven't distinguished left-open and right-open because that'd just be weird.
- empty: Null polytope (Null polytope)
- degenerate: Point (Point)
- proper and bounded:
- left-bounded and right-unbounded:
- left-unbounded and right-bounded:
- unbounded at both ends (simultaneously open and closed): : Euclidean line (Euclidean line)