ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Basic binary operation
Unsigned basic binary operation
Semimetric
Metric
Metric space
Set distance
Closed ball
Definition D1401
Sphere
Formulation 0
Let $M = (X, d)$ be a D1107: Metric space.
The sphere in $M$ with centre $E \subseteq X$ and radius $r \in (0, \infty)$ is the D11: Set \begin{equation} S_d(E, r) : = \{ x \in X : d(E, x) = r \} \end{equation}