4. Balls and spheres

4.1 The spheres in ...

Title : Spheres in $ℤ^{n}$

A sphere S ⁿ^–1 (x,r) of center x and radius r in the n-dimensional set $ℤ^{n}$ of all numbers of relative integers (n ≥ 1), provided with the distance induced by the Euclidean distance, can be empty (unlike the corresponding ball B ⁿ (x,r)). Indeed, such a sphere is non-empty if and only if its radius r can...

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Balls and spheres

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Bibliography

(1) - AARTS (J.M.), NISHIURA (T.) - Dimension and Extensions, - North Holland, 331 pages (1993).
(2) - ADAMS (C.), FRANZOSA (R.) - Introduction to Topology Pure and Applied, - Pearson, 507 pages (2008).
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