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Difference between revisions of "Universal covering"

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A [[Covering|covering]] to which every other covering is subordinate.
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A [[covering]] to which every other covering is subordinate.
  
  
  
 
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A covering <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095660/u0956601.png" /> of a space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095660/u0956602.png" /> is subordinate to a covering <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095660/u0956603.png" /> if there is a covering <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095660/u0956604.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/u/u095/u095660/u0956605.png" />.
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A covering $p:X\rightarrow Y$ of a space $Y$ is ''subordinate'' to a covering $p':X'\rightarrow Y$ if there is a covering $f:X'\rightarrow X$ such that $p'=pf$.
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Latest revision as of 20:01, 10 December 2017

A covering to which every other covering is subordinate.


Comments

A covering $p:X\rightarrow Y$ of a space $Y$ is subordinate to a covering $p':X'\rightarrow Y$ if there is a covering $f:X'\rightarrow X$ such that $p'=pf$.

How to Cite This Entry:
Universal covering. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Universal_covering&oldid=11638
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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