| 释义 |
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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 in the sense that there does not exist an ambient isotopy taking the arc to a straight line segment. {{harvtxt|Antoine|1920}} found the first example of a wild arc, and {{harvtxt|Fox|Artin|1948}} found another example called the Fox–Artin arc whose complement is not simply connected. See alsoFurther reading- {{citation|first=L.|last=Antoine|title=Sur la possibilité d'étendre l'homéomorphie de deux figures à leurs voisinages|journal=C. R. Acad. Sci. Paris|year=1920|volume=171|page=661}}
- {{Citation | last1=Fox | first1=Ralph H. | last2=Harrold | first2=O. G. | title=Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) | publisher=Prentice Hall | mr=0140096 | year=1962 | chapter=The Wilder arcs | pages=184–187}}
- {{Citation | last1=Fox | first1=Ralph H. |author1-link=Ralph Fox| last2=Artin | first2=Emil | author2-link=Emil Artin | title=Some wild cells and spheres in three-dimensional space | jstor=1969408 | mr=0027512 | year=1948 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=49 | pages=979–990 | doi=10.2307/1969408}}
- {{cite book|ref=harv|first1=John Gilbert|last1=Hocking|first2=Gail Sellers|last2=Young|title=Topology|year=1988|origyear=1961|publisher=Dover|isbn=0-486-65676-4|pages=176–177}}
- {{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 | mr=0343276 | year=1973 | journal=Pacific Journal of Mathematics | issn=0030-8730 | volume=45 | pages=585–598 | doi=10.2140/pjm.1973.45.585}}
1 : Geometric topology |