Difference between revisions of "Aspherical space"

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{{topospace property}}
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{{homotopy-invariant topospace property}}
  
 
==Definition==
 
==Definition==
  
 
A [[topological space]] is termed '''aspherical''' if it possesses a [[universal covering space]], and if its universal covering space is [[weakly contractible space|weakly contractible]] (equivalently the universal covering space is [[acyclic space|acyclic]]; for path-connected simply connected spaces, the two notions are equivalent).
 
A [[topological space]] is termed '''aspherical''' if it possesses a [[universal covering space]], and if its universal covering space is [[weakly contractible space|weakly contractible]] (equivalently the universal covering space is [[acyclic space|acyclic]]; for path-connected simply connected spaces, the two notions are equivalent).

Revision as of 00:00, 2 December 2007

This article defines a homotopy-invariant property of topological spaces, i.e. a property of homotopy classes of topological spaces


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Definition

A topological space is termed aspherical if it possesses a universal covering space, and if its universal covering space is weakly contractible (equivalently the universal covering space is acyclic; for path-connected simply connected spaces, the two notions are equivalent).