@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:-KFSNTTXP-S
  skos:prefLabel "general topology"@en, "topologie générale"@fr ;
  a skos:Concept ;
  skos:narrower psr:-D0STC250-J .

psr:-MGJVTWX1-0
  skos:prefLabel "espace topologique"@fr, "topological space"@en ;
  a skos:Concept ;
  skos:narrower psr:-D0STC250-J .

psr:-D0STC250-J
  a skos:Concept ;
  dc:created "2023-07-24"^^xsd:date ;
  skos:prefLabel "adjunction space"@en, "recollement"@fr ;
  skos:inScheme psr: ;
  skos:broader psr:-MGJVTWX1-0, psr:-KFSNTTXP-S ;
  skos:definition """In mathematics, an <b>adjunction space</b> (or <b>attaching space</b>) is a common construction in topology where one topological space is attached or "glued" onto another. Specifically, let <i>X</i> and <i>Y</i> be topological spaces, and let <i>A</i> be a subspace of <i>Y</i>. Let <i>f</i>&nbsp;: <i>A</i> → <i>X</i> be a continuous map (called the <b>attaching map</b>). One forms the adjunction space <i>X</i> ∪<sub><i>f</i></sub> <i>Y</i> (sometimes also written as <i>X</i> +<sub><i>f</i></sub> <i>Y</i>) by taking the disjoint union of <i>X</i> and <i>Y</i> and identifying <i>a</i> with <i>f</i>(<i>a</i>) for all <i>a</i> in <i>A</i>. Formally,
<br/>
<br/><dl><dd><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 X\\\\cup _{f}Y=(X\\\\sqcup Y)/\\\\sim }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>X</mi>
<br/>        <msub>
<br/>          <mo>∪<!-- ∪ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>f</mi>
<br/>          </mrow>
<br/>        </msub>
<br/>        <mi>Y</mi>
<br/>        <mo>=</mo>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>X</mi>
<br/>        <mo>⊔<!-- ⊔ --></mo>
<br/>        <mi>Y</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mo>/</mo>
<br/>        </mrow>
<br/>        <mo>∼<!-- ∼ --></mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle X\\\\cup _{f}Y=(X\\\\sqcup Y)/\\\\sim }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d264070f8fa125b70e4d9a51918eef53fb1b7c0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.005ex; width:22.332ex; height:3.009ex;" alt="{\\\\displaystyle X\\\\cup _{f}Y=(X\\\\sqcup Y)/\\\\sim }"></span></dd></dl>
<br/>where the equivalence relation ~ is generated by <i>a</i> ~ <i>f</i>(<i>a</i>) for all <i>a</i> in <i>A</i>, and the quotient is given the quotient topology. As a set, <i>X</i> ∪<sub><i>f</i></sub> <i>Y</i> consists of the disjoint union of <i>X</i> and (<i>Y</i> − <i>A</i>). The topology, however, is specified by the quotient construction. 
<br/>Intuitively, one may think of <i>Y</i> as being glued onto <i>X</i> via the map <i>f</i>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Adjunction_space">https://en.wikipedia.org/wiki/Adjunction_space</a>)"""@en, """En mathématiques, le recollement est la construction d'un espace topologique obtenu en « attachant un espace à un autre le long d'une application ». Plus précisément on attache un espace <i>Y</i> à un espace <i>X</i>, le long d'une application <i>f</i> à valeurs dans <i>X</i>, continue sur un sous-espace <i>A</i> de <i>Y</i>, en définissant l'espace <i>X </i>∪<i><sub>f</sub> Y </i> comme le quotient de la somme topologique <i>X</i>⊔<i>Y</i> par la relation d'équivalence qui identifie chaque élément de <i>A</i> à son image par <i>f</i>. C'est un cas particulier de somme amalgamée. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Recollement_(topologie)">https://fr.wikipedia.org/wiki/Recollement_(topologie)</a>)"""@fr ;
  dc:modified "2023-07-24"^^xsd:date ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Recollement_(topologie)>, <https://en.wikipedia.org/wiki/Adjunction_space> .