A Manifold
<ol style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; list-style-position: inside; list-style-image: initial; color: rgb(34, 34, 34);"><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">now historical</span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> A <a href="https://en.m.wiktionary.org/wiki/copy" title="copy" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">copy</a> made by the manifold writing process.</li><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/mechanics" title="mechanics" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">mechanics</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> A pipe <a href="https://en.m.wiktionary.org/wiki/fitting" title="fitting" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">fitting</a> or similar <a href="https://en.m.wiktionary.org/wiki/device" title="device" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">device</a>that connects multiple <a href="https://en.m.wiktionary.org/wiki/input" title="input" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">inputs</a> or <a href="https://en.m.wiktionary.org/wiki/output" title="output" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">outputs</a>.</li><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.wikipedia.org/wiki/United_States" class="extiw" title="w:United States" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">US</a><span class="ib-comma" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">,</span> regional<span class="ib-comma" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">,</span> in the <a href="https://en.m.wiktionary.org/wiki/Appendix:Glossary#plural" title="Appendix:Glossary" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">plural</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> The third <a href="https://en.m.wiktionary.org/wiki/stomach" title="stomach" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">stomach</a> of a <a href="https://en.m.wiktionary.org/wiki/ruminant" title="ruminant" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">ruminant</a> animal, an <a href="https://en.m.wiktionary.org/wiki/omasum" title="omasum" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">omasum</a>.</li><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/mathematics" title="mathematics" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">mathematics</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> A <a href="https://en.m.wiktionary.org/wiki/topological_space" title="topological space" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">topological space</a> that looks <a href="https://en.m.wiktionary.org/wiki/local" title="local" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">locally</a> like the "ordinary" <a href="https://en.m.wiktionary.org/wiki/Euclidean_space" title="Euclidean space" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">Euclidean space</a> <span class="mwe-math-element" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; display: none; clip: rect(1px, 1px, 1px, 1px); overflow: hidden; position: absolute; width: 1px; height: 1px; opacity: 0;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"><semantics><annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation></semantics></math></span><img width="0" height="0" class="mwe-math-fallback-image-inline image-lazy-loaded" alt="{\displaystyle \mathbb {R} ^{n}}" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" srcset="" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: middle; background: none; display: inline-block; animation: 0.3s ease-in 0s 1 normal none running fadeInImage; width: 2.897ex; height: 2.343ex;"></span> and is <a href="https://en.m.wiktionary.org/wiki/Hausdorff" title="Hausdorff" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">Hausdorff</a>.</li><li style="margin-top: 0px; margin-right: 0px; margin-bottom: inherit; margin-left: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/computer_graphics" title="computer graphics" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">computer graphics</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> A <a href="https://en.m.wiktionary.org/wiki/polygon_mesh" title="polygon mesh" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">polygon mesh</a>representing the continuous, closed surface of a solid object</li></ol><h5 class="in-block" style="margin: 0px; padding: 0.5em 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-weight: inherit; font-stretch: inherit; line-height: 1.3; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; font-size: 16px; vertical-align: baseline; background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; overflow-wrap: break-word; word-break: break-word; display: table; color: rgb(34, 34, 34);"><span class="mw-headline" id="Usage_notes" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: middle; background: none; display: table-cell; width: 272px;">Usage notes</span><span class="mw-editsection" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: middle; background: none; display: table-cell;"><a href="https://en.m.wiktionary.org/w/index.php?title=manifold&action=edit&section=6" title="Edit section: Usage notes" data-section="6" class="mw-ui-icon mw-ui-icon-element mw-ui-icon-minerva-edit-enabled edit-page" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: 1.5em; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161); position: relative; min-height: 1.5em; min-width: 3.5em; text-indent: -999px; overflow: hidden; width: 3.5em; max-width: 3.5em; display: block;">Edit</a></span></h5><p style="margin: 0.5em 0px 1em; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; color: rgb(34, 34, 34);">In mathematics, a manifold of some number of dimensions <i style="margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">n</i> is termed an <i style="margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">n-manifold</i> (e.g. <i style="margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">3-manifold</i>).</p>