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 ${\displaystyle S^{1}\times D^{2}}$ 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 ${\displaystyle S^{1}\times S^{1}}$, the ordinary torus.

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