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Article | REF: AF123 V1

Examples in Topology II. Products Spaces, Vector Spaces, Sequence Spaces, Function Spaces, and Subset Spaces

Author: Jean-Charles PINOLI

Publication date: October 10, 2018, Review date: May 7, 2021

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4. Balls and spheres

4.1 The spheres in ...

Title : Spheres in ℤn

A sphere S n –1 (x,r) of center x and radius r in the n-dimensional set ℤn 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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