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

psr:-RHXBWN0G-4
  skos:prefLabel "anneau"@fr, "ring"@en ;
  a skos:Concept ;
  skos:narrower psr:-RHLZBQJ3-1 .

psr:-KBM0D7VN-X
  skos:prefLabel "anneau adélique"@fr, "adele ring"@en ;
  a skos:Concept ;
  skos:broader psr:-RHLZBQJ3-1 .

psr:-LHPGDNPG-6
  skos:prefLabel "corps valué"@fr, "valuation"@en ;
  a skos:Concept ;
  skos:broader psr:-RHLZBQJ3-1 .

psr: a skos:ConceptScheme .
psr:-RHLZBQJ3-1
  skos:broader psr:-RHXBWN0G-4 ;
  skos:definition """En mathématiques, un anneau topologique est un anneau muni d'une topologie compatible avec les opérations internes, c'est-à-dire telle que l'addition, l'application opposée et la multiplication soient continues. Un corps topologique est un corps muni d'une topologie qui rend continues l'addition, la multiplication et l'application inverse. Ces structures étendent la notion de groupe topologique. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Anneau_topologique">https://fr.wikipedia.org/wiki/Anneau_topologique</a>)"""@fr, """In mathematics, a <b>topological ring</b> is a ring <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 R}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>R</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle R}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="R"></span> that is also a topological space such that both the addition and the multiplication are continuous as maps:
         <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 R\\	imes R\\	o R}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>R</mi>
         <mo>×<!-- × --></mo>
         <mi>R</mi>
         <mo stretchy="false">→<!-- → --></mo>
         <mi>R</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle R\\	imes R\\	o R}</annotation>
         </semantics>
         </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a34b3a1fac851bcff3ba56b027cb4a27f485f885" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.746ex; height:2.176ex;" alt="{\\\\displaystyle R\\	imes R\\	o R}"></div>
         where <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 R\\	imes R}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>R</mi>
         <mo>×<!-- × --></mo>
         <mi>R</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle R\\	imes R}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db84aa6eea31c7dc5fba640b32acddbb579c592d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.368ex; height:2.176ex;" alt="{\\\\displaystyle R\\	imes R}"></span> carries the product topology. That means <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 R}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>R</mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle R}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="R"></span> is an additive topological group and a multiplicative topological semigroup.
         Topological rings are fundamentally related to topological fields and arise naturally while studying them, since for example completion of a topological field may be a topological ring which is not a field.
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Topological_ring">https://en.wikipedia.org/wiki/Topological_ring</a>)"""@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Anneau_topologique>, <https://en.wikipedia.org/wiki/Topological_ring> ;
  skos:inScheme psr: ;
  skos:narrower psr:-LHPGDNPG-6, psr:-KBM0D7VN-X ;
  a skos:Concept ;
  skos:prefLabel "topological ring"@en, "anneau topologique"@fr .