@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-CF5FC8JW-T
  skos:prefLabel "espace vectoriel normé"@fr, "normed vector space"@en ;
  a skos:Concept ;
  skos:narrower psr:-Q49K3SG4-S .

psr:-Q49K3SG4-S
  skos:exactMatch <https://en.wikipedia.org/wiki/Banach_lattice> ;
  skos:broader psr:-G154H5ZN-5, psr:-CF5FC8JW-T ;
  dc:modified "2023-08-18"^^xsd:date ;
  skos:prefLabel "Banach lattice"@en, "treillis de Banach"@fr ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:altLabel "réseau de Banach"@fr ;
  skos:definition """In the mathematical disciplines of in functional analysis and order theory, a <b>Banach lattice</b> <span class="texhtml">(<i>X</i>,‖·‖)</span> is a complete normed vector space with a lattice order, such that for all <span class="texhtml"><i>x</i>, <i>y</i> ∈ <i>X</i></span>, the implication <div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {|x|\\\\leq |y|}\\\\Rightarrow {\\\\|x\\\\|\\\\leq \\\\|y\\\\|}}">
         <semantics>
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         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
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         <mo stretchy="false">|</mo>
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         <mi>x</mi>
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         <mo>≤<!-- ≤ --></mo>
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         <mi>y</mi>
         <mo fence="false" stretchy="false">‖<!-- ‖ --></mo>
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         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle {|x|\\\\leq |y|}\\\\Rightarrow {\\\\|x\\\\|\\\\leq \\\\|y\\\\|}}</annotation>
         </semantics>
         </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6917b88005f16d66d4174b94f4ab03d0cce66488" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.019ex; height:2.843ex;" alt="{\\\\displaystyle {|x|\\\\leq |y|}\\\\Rightarrow {\\\\|x\\\\|\\\\leq \\\\|y\\\\|}}"></div> holds, where the absolute value <span class="texhtml">|·|</span> is defined as <div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle |x|=x\\\\vee -x{\\	ext{.}}}">
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         <annotation encoding="application/x-tex">{\\\\displaystyle |x|=x\\\\vee -x{\\	ext{.}}}</annotation>
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         </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e933640bff130db53d737d0386900fc0605116ee" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.419ex; height:2.843ex;" alt="{\\\\displaystyle |x|=x\\\\vee -x{\\	ext{.}}}"></div>  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Banach_lattice">https://en.wikipedia.org/wiki/Banach_lattice</a>)"""@en .

psr:-G154H5ZN-5
  skos:prefLabel "treillis"@fr, "lattice"@en ;
  a skos:Concept ;
  skos:narrower psr:-Q49K3SG4-S .