File:EANear and eAMer Supercategories.png
Summary
<img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48861a1593d8e90b777a5d547f608accb8232976" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:9.688ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\varepsilon {ANear}}}}"> and <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/849ae45b58303f5308d67683b7c811f722022c0d" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:8.652ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\varepsilon {AMer}}}}"> are shown to be full supercategories of various well-known categories, including the category <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45a0410e818c6988e13637ad91bed47e82c14c04" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:5.827ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {sTop}}}"> of symmetric topological spaces and continuous maps, and the category <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a331fd029a9e5e56a47a908e6ad31cba3ddcb65" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:7.246ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {Met^{\infty }}}}"> of extended metric spaces and nonexpansive maps.
Licensing
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:29, 7 January 2017 | | 794 × 660 (32 KB) | 127.0.0.1 (talk) | <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold-italic">ε<!-- ε --></mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold-italic">A</mi><mi mathvariant="bold-italic">N</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">a</mi><mi mathvariant="bold-italic">r</mi></mrow></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\varepsilon {ANear}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48861a1593d8e90b777a5d547f608accb8232976" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:9.688ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\varepsilon {ANear}}}}"></span> and <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold-italic">ε<!-- ε --></mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold-italic">A</mi><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">r</mi></mrow></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\varepsilon {AMer}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/849ae45b58303f5308d67683b7c811f722022c0d" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:8.652ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\varepsilon {AMer}}}}"></span> are shown to be full supercategories of various well-known categories, including the category <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold-italic">s</mi><mi mathvariant="bold-italic">T</mi><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">p</mi></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {sTop}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45a0410e818c6988e13637ad91bed47e82c14c04" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:5.827ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {sTop}}}"></span> of symmetric topological spaces and continuous maps, and the category <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold-italic">M</mi><mi mathvariant="bold-italic">e</mi><msup><mi mathvariant="bold-italic">t</mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">∞<!-- ∞ --></mi></mrow></msup></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {Met^{\infty }}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a331fd029a9e5e56a47a908e6ad31cba3ddcb65" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:7.246ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {Met^{\infty }}}}"></span> of extended metric spaces and nonexpansive maps. |
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