Difference between revisions of "Simple space"

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{{topospace property}}
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{{homotopy-invariant topospace property}}
  
 
==Definition==
 
==Definition==
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* It is [[path-connected space|path-connected]]
 
* It is [[path-connected space|path-connected]]
 
* The [[fundamental group]] is [[Abelian group|Abelian]]
 
* The [[fundamental group]] is [[Abelian group|Abelian]]
* The fundamental group acts trivially on all the higher homotopy groups
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* The fundamental group [[actions of the fundamental group|acts]] trivially on all the higher homotopy groups
  
 
==Relation with other properties==
 
==Relation with other properties==
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* [[Simply connected space]]
 
* [[Simply connected space]]
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* [[Aspherical space]] with Abelian fundamental group
  
 
===Weaker properties===
 
===Weaker properties===
  
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* [[Space with Abelian fundamental group]]
 
* [[Path-connected space]]
 
* [[Path-connected space]]
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==References==
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===Textbook references===
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* {{booklink|Concise}}, Page 140 (formal definition)
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* {{booklink|Hatcher}}, Page 342 (definition in paragraph): Hatcher uses the term '''Abelian space''' locally in the book
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* {{booklink|Spanier}}, Page 384 (definition in paragraph)

Latest revision as of 19:58, 11 May 2008

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


View other homotopy-invariant properties of topological spaces OR view all properties of topological spaces

Definition

A topological space is termed simple if it satisfies the following three conditions:

Relation with other properties

Stronger properties

Weaker properties

References

Textbook references

  • A Concise Course in Algebraic Topology by J Peter MayFull text PDFMore info, Page 140 (formal definition)
  • Algebraic Topology by Allen HatcherFull text PDFMore info, Page 342 (definition in paragraph): Hatcher uses the term Abelian space locally in the book
  • Algebraic Topology by Edwin H. SpanierMore info, Page 384 (definition in paragraph)