Solid torus

In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle. It is homeomorphic to the Cartesian product S 1 × D 2 {displaystyle S^{1} imes D^{2}} of the disk and the circle, endowed with the product topology.A standard way to visualize a solid torus is as a toroid, embedded in 3-space. However, it should be distinguished from a torus, which has the same visual appearance: the torus is the two-dimensional space on the boundary of a toroid, while the solid torus includes also the compact interior space enclosed by the torus.The solid torus is a connected, compact, orientable 3-dimensional manifold with boundary. The boundary is homeomorphic to S 1 × S 1 {displaystyle S^{1} imes S^{1}}  , the ordinary torus.