In Euclidean n-space, an (open) n-ball of radius r and center x is the set of all points of distance less than r from x. A closed n-ball of radius r is the set of … 展开

One may talk about balls in any topological space X, not necessarily induced by a metric. An (open or closed) n-dimensional topological … 展开

• Ball – ordinary meaning
• Disk (mathematics)
• Formal ball, an extension to negative radii
• Neighbourhood (mathematics) 展开

Let (M, d) be a metric space, namely a set M with a metric (distance function) d, and let ⁠ $${\displaystyle r}$$ ⁠ be a positive real number. The open (metric) … 展开

Any normed vector space V with norm $${\displaystyle \|\cdot \|}$$ is also a metric space with the metric $${\displaystyle d(x,y)=\|x-y\|.}$$ In such spaces, an arbitrary ball $${\displaystyle B_{r}(y)}$$ of points $${\displaystyle x}$$ around a point 展开

A number of special regions can be defined for a ball:
• cap, bounded by one plane
• sector, bounded by a conical boundary with apex at the center of … 展开