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In geometric topology, a '''wild arc''' is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one. The first example was the '''Fox-Artin arc''' found by {{harvtxt|Fox|Artin|1948}}. |
In geometric topology, a '''wild arc''' is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one. The first example was found by L. Antoine in 1920, and the '''Fox-Artin arc''' was found by {{harvtxt|Fox|Artin|1948}}. |
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==References== |
==References== |
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*{{Citation | last1=Fox | first1=Ralph H. | last2=Artin | first2=Emil | author2-link=Emil Artin | title=Some wild cells and spheres in three-dimensional space | url=http://www.jstor.org/stable/1969408 | id={{MathSciNet | id = 0027512}} | year=1948 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=49 | pages=979–990}} |
*{{Citation | last1=Fox | first1=Ralph H. | last2=Artin | first2=Emil | author2-link=Emil Artin | title=Some wild cells and spheres in three-dimensional space | url=http://www.jstor.org/stable/1969408 | id={{MathSciNet | id = 0027512}} | year=1948 | journal=[[Annals of Mathematics|Annals of Mathematics. Second Series]] | issn=0003-486X | volume=49 | pages=979–990}} |
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*{{Citation | last1=McPherson | first1=James M. | title=Wild arcs in three-space. I. Families of Fox-Artin arcs | url=http://projecteuclid.org/euclid.pjm/1102947540 | id={{MathSciNet | id = 0343276}} | year=1973 | journal=[[Pacific Journal of Mathematics]] | issn=0030-8730 | volume=45 | pages=585–598}} |
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[[Category:geometric topology]] |
[[Category:geometric topology]] |
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Revision as of 17:10, 18 January 2010
In geometric topology, a wild arc is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one. The first example was found by L. Antoine in 1920, and the Fox-Artin arc was found by Fox & Artin (1948).
References
- Fox, Ralph H.; Artin, Emil (1948), "Some wild cells and spheres in three-dimensional space", Annals of Mathematics. Second Series, 49: 979–990, ISSN 0003-486X, MR0027512
- McPherson, James M. (1973), "Wild arcs in three-space. I. Families of Fox-Artin arcs", Pacific Journal of Mathematics, 45: 585–598, ISSN 0030-8730, MR0343276