KLEIN BOTTLE

topological space, named for the German mathematician Felix Klein, obtained by identifying two ends of a cylindrical surface in the direction opposite that is necessary to obtain a torus. The surface is not constructible in three-dimensional Euclidean space but has interesting properties, such as being one-sided, like the Mbius strip (q.v.); being closed, yet having no inside like a torus or a sphere; and resulting in two Mbius strips if properly cut in two.