Question

What is an open ball

Answer 1

Answer:

An n-dimensional open ball of radius r is the collection of points of distance less than r from a fixed point in Euclidean n-space. Explicitly, the open ball with center x and radius r is defined by

B_r(x)={y:|y-x|<r}.  

The open ball for n=1 is called an open interval, and the term open disk is sometimes used for n=2 and sometimes as a synonym for open ball.

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Answer 2

In mathematics, a ball is the space bounded by a sphere. It may be a closed ball or an open ball. These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general.