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an open n-ball B and ℝn can be classified in two classes, that can be identified with the two possible topological orientations of B. A topological n-ballIn mathematics, a ball is the volume space bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ball or hyperball in n dimensions is called an n-ball and is bounded by an (n − 1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a line segment. In other contexts, such as in Euclidean geometry and informal use, sphere is sometimes used to mean ball.