<span class="math inline">\(n\)</span>-dimensional
basis for <span class="math inline">\(S^{n-1}\)</span> that preserves local neighborhoods in that points
that are close to each other in <span class="math inline">\(\mathbb{R}^n\)</span> map to points near each
other in <span class="math inline">\(S^{n-1}\)</span>. The mapping is not perfectly distance preserving,
because there are points arbitrarily far away from each other in
<span class="math inline">\(\mathbb{R}^n\)</span> that map to identical points i