@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-R1XTRSBL-Q
  skos:prefLabel "variété de Stiefel"@fr, "Stiefel manifold"@en ;
  a skos:Concept ;
  skos:broader psr:-CZK7R9T1-N .

psr:-CZK7R9T1-N
  a skos:Concept ;
  skos:narrower psr:-TCRDC7FL-J, psr:-BX3NBRCV-X, psr:-R1XTRSBL-Q, psr:-F875HNKG-J ;
  skos:prefLabel "fiber bundle"@en, "espace fibré"@fr ;
  skos:definition """En mathématiques, un espace fibré est, intuitivement, un espace topologique qui est localement le produit de deux espaces — appelés la base et la fibre — mais en général pas globalement. Par exemple, le ruban de Möbius est un fibré de base un cercle et de fibre un segment de droite : il ressemble localement au produit d'un cercle par un segment, mais pas globalement comme le cylindre. Plus précisément, l'espace total du fibré est muni d'une projection continue sur la base, telle que la préimage de chaque point soit homéomorphe à la fibre. Cette projection est a priori supposée localement triviale, c'est-à-dire que tout point de la base admet un voisinage dont la préimage s'identifie à un produit cartésien de ce voisinage et de la fibre, par le biais d'homéomorphismes appelés trivialisations ou cartes. Le passage d'une trivialisation à l'autre se fait au moyen d'un groupe d'homéomorphismes de la fibre appelé groupe de structure. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Fibr%C3%A9">https://fr.wikipedia.org/wiki/Fibr%C3%A9</a>)"""@fr, """In mathematics, and particularly topology, a <b>fiber bundle</b> (or, in Commonwealth English: <b>fibre bundle</b>) is a space that is <em>locally</em> a product space, but <em>globally</em> may have a different topological structure. Specifically, the similarity between a space <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>E</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle E}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="E"></span> and a product space <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle B\\	imes F}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>B</mi>
         <mo>×<!-- × --></mo>
         <mi>F</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle B\\	imes F}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05e0fcb90530d44152eea7eb002ee9b1278c7165" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.345ex; height:2.176ex;" alt="{\\\\displaystyle B\\	imes F}"></span> is defined using a continuous surjective map, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\pi :E\\	o B,}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>π<!-- π --></mi>
         <mo>:</mo>
         <mi>E</mi>
         <mo stretchy="false">→<!-- → --></mo>
         <mi>B</mi>
         <mo>,</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\pi :E\\	o B,}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4858e5871a48062c0d5e3fe6b11b999f1b646459" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.07ex; height:2.509ex;" alt="{\\\\displaystyle \\\\pi :E\\	o B,}"></span> that in small regions of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>E</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle E}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="E"></span> behaves just like a projection from corresponding regions of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle B\\	imes F}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>B</mi>
         <mo>×<!-- × --></mo>
         <mi>F</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle B\\	imes F}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05e0fcb90530d44152eea7eb002ee9b1278c7165" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.345ex; height:2.176ex;" alt="{\\\\displaystyle B\\	imes F}"></span> to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle B.}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>B</mi>
         <mo>.</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle B.}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0eccf5bca7cdc1fa4439af2d31831db6bde00473" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.411ex; height:2.176ex;" alt="B."></span>  The map <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\pi ,}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>π<!-- π --></mi>
         <mo>,</mo>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\pi ,}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47495546dd4b7607bbcb5658efe66abaf1955034" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.979ex; height:2.009ex;" alt="\\\\pi,"></span> called the <b>projection</b> or <b>submersion</b> of the bundle, is regarded as part of the structure of the bundle.  The space <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle E}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>E</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle E}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="E"></span> is known as the <b>total space</b> of the fiber bundle, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle B}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>B</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle B}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="B"></span> as the <b>base space</b>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle F}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>F</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle F}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="F"></span> the <b>fiber</b>.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Fiber_bundle">https://en.wikipedia.org/wiki/Fiber_bundle</a>)"""@en ;
  skos:inScheme psr: ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Fiber_bundle>, <https://fr.wikipedia.org/wiki/Fibr%C3%A9> ;
  skos:broader psr:-MGJVTWX1-0 ;
  skos:altLabel "fibre bundle"@en, "fibré"@fr .

psr:-TCRDC7FL-J
  skos:prefLabel "champ vectoriel fondamental"@fr, "fundamental vector field"@en ;
  a skos:Concept ;
  skos:broader psr:-CZK7R9T1-N .

psr:-BX3NBRCV-X
  skos:prefLabel "covering space"@en, "revêtement"@fr ;
  a skos:Concept ;
  skos:broader psr:-CZK7R9T1-N .

psr:-F875HNKG-J
  skos:prefLabel "fibré principal"@fr, "principal bundle"@en ;
  a skos:Concept ;
  skos:broader psr:-CZK7R9T1-N .

psr: a skos:ConceptScheme .
psr:-MGJVTWX1-0
  skos:prefLabel "espace topologique"@fr, "topological space"@en ;
  a skos:Concept ;
  skos:narrower psr:-CZK7R9T1-N .