Like the
Möbius strip, the Klein bottle is a two-dimensional
manifold which is not
orientable. Unlike the Möbius strip, it is a
closed manifold, meaning it is a
compact manifold without boundary. While the Möbius strip can be embedded in three-dimensional
Euclidean space R3, the Klein bottle cannot. It can be embedded in
R4, however.
[4]
Continuing this sequence, for example creating a 3-manifold which cannot be embedded in
R4 but can be in
R5, is possible; in this case, connecting two ends of a
spherinder to each other in the same manner as the two ends of a cylinder for a Klein bottle, creates a figure, referred to as a "spherinder Klein bottle", that cannot fully be embedded in
R4.
[5]