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Metric Space Circle Euclidean Distance Euclidean Vector Space Empty Set Even Number Connected Space Discrete Word Hexahedron Center Of A Triangle

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Sphere Metric Space

The set $\{ x \mid d(x,c) = r \}$ is called the sphere of radius with centre . This generalizes the notion of spheres to metric spaces.

Note that the sphere in a metric space need not look like a sphere in Euclidean space. For instance, if we impose the metric $d(x,y) = max \{\vert x_1-y_1\vert, \vert x_2-y_2\vert, \vert x_3-y_3\vert\}$ on $\mathbb{R}^3$ instead of the Euclidean metric, spheres according to this metric are actually cubes! Even more bizarre situations can occur in general -- a sphere might be disconnected, or it may be discrete, or it may even be an empty set.

1	Circle
1	Euclidean Vector Space
1	Metric Space
1	Euclidean Distance
1	Empty Set
1	Even Number
2	Discrete
2	Connected Space
2	Word
4	Hexahedron
5	Center Of A Triangle