Metric-Spaces on Chen Kai Bloghttps://www.chenk.top/en/tags/metric-spaces/Recent content in Metric-Spaces on Chen Kai BlogHugoenFri, 01 Oct 2021 09:00:00 +0000Functional Analysis (1): Metric Spaces — Distance, Convergence, and Completenesshttps://www.chenk.top/en/functional-analysis/01-metric-spaces/Fri, 01 Oct 2021 09:00:00 +0000https://www.chenk.top/en/functional-analysis/01-metric-spaces/<h2 id="why-i-had-to-stop-trusting-my-finite-dimensional-intuition" class="heading-anchor">Why I Had to Stop Trusting My Finite-Dimensional Intuition<a href="#why-i-had-to-stop-trusting-my-finite-dimensional-intuition" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><p>The first thing graduate analysis did to me was take away my picture. Up to that point, &ldquo;distance&rdquo; had always been the length of an arrow drawn from the origin to a point — Pythagoras, three coordinates, done. Then somebody asked me how far two functions are from each other and the arrow disappeared.</p>