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article. Example 1.1 (page 981) is most generally referred to as the Fox-Artin wild arc. The crossings have the regular sequence over/over/under/over/under/under when following the curve from left to right.
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is mapped by the arc to the left limit point of the curve, and 1 is mapped to the right limit point. The range of the arc lies in the
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20:
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73:
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Antoine, L. (1920), "Sur la possibilité d'étendre l'homéomorphie de deux figures à leurs voisinages",
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into 3-dimensional space not equivalent to the usual one in the sense that there does not exist an
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Example 1.1* has the crossing sequence over/under/over/under/over/under. According to
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Embedding of the unit interval into 3-space ambient isotopy inequivalent to a line segment
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Topology of 3-manifolds and related topics (Proc. The Univ. of
Georgia Institute, 1961)
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Also shown here is an alternative style of diagram for the arc in
Example 1.1*.
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This article is about a mathematical object. For animal rehabilitation, see
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This arc cannot be continuously deformed to produce
Example 1.1 in
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388:(1948), "Some wild cells and spheres in three-dimensional space",
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26:
508:
463:"Wild arcs in three-space. I. Families of Fox–Artin arcs"
317:. Note that each "tail" of the arc is converging to a point.
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Fox, Ralph H.; Harrold, O. G. (1962), "The Wilder arcs",
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169:
137:
102:
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Hocking, John
Gilbert; Young, Gail Sellers (1988) .
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The Fox–Artin wild arc (Example 1.1*) lying in
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96:The left end-point 0 of the closed unit interval
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218:extended indefinitely in both directions."
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88:Two very similar wild arcs appear in the
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64:found the first example of a wild arc.
61:
7:
210:, page 982: "This is just the
277:, despite its similar appearance.
68:found another example, called the
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21:Wild Animal Rehabilitation Center
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306:{\displaystyle \mathbb {R} ^{3}}
243:{\displaystyle \mathbb {R} ^{3}}
153:{\displaystyle \mathbb {R} ^{3}}
468:Pacific Journal of Mathematics
115:
103:
1:
461:McPherson, James M. (1973),
58:to a straight line segment.
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781:Banach fixed-point theorem
202:Fox-Artin arc Example 1.1*
18:
814:
610:
30:Fox-Artin arc Example 1.1
482:10.2140/pjm.1973.45.585
336:Alexander horned sphere
836:Mathematics portal
736:Metrics and properties
722:Second-countable space
350:C. R. Acad. Sci. Paris
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208:Fox & Artin (1948)
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90:Fox & Artin (1948)
66:Fox & Artin (1948)
31:
391:Annals of Mathematics
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270:{\displaystyle S^{3}}
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201:
194:Fox-Artin arc variant
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183:{\displaystyle S^{3}}
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791:Invariance of domain
743:Euler characteristic
717:Bundle (mathematics)
369:, pp. 184–187,
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135:
100:
801:Tychonoff's theorem
796:Poincaré conjecture
550:General (point-set)
914:Geometric topology
786:De Rham cohomology
707:Polyhedral complex
697:Simplicial complex
442:. Dover. pp.
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36:geometric topology
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690:fundamental group
394:, Second Series,
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121:{\displaystyle }
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78:simply connected
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342:Further reading
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52:ambient isotopy
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475:(2): 585–598,
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398:(4): 979–990,
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62:Antoine (1920)
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763:Orientability
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382:Fox, Ralph H.
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367:Prentice Hall
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352:(in French),
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70:Fox-Artin arc
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48:unit interval
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893:Publications
758:Chern number
748:Betti number
631: /
622:Key concepts
570:Differential
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320:
315:knot diagram
220:
212:chain stitch
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39:
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856:Wikiversity
773:Key results
386:Artin, Emil
313:drawn as a
54:taking the
702:CW complex
643:Continuity
633:Closed set
592:cohomology
74:complement
881:geometric
876:algebraic
727:Cobordism
663:Hausdorff
658:connected
575:Geometric
565:Continuum
555:Algebraic
491:0030-8730
412:0003-486X
331:Wild knot
44:embedding
908:Category
846:Wikibook
824:Category
712:Manifold
680:Homotopy
638:Interior
629:Open set
587:Homology
536:Topology
438:Topology
325:See also
216:knitting
162:3-sphere
72:, whose
40:wild arc
871:general
673:uniform
653:compact
604:Digital
499:0343276
444:176–177
428:0027512
420:1969408
375:0140096
160:or the
76:is not
46:of the
866:Topics
668:metric
543:Fields
497:
489:
450:
426:
418:
410:
373:
42:is an
648:Space
416:JSTOR
356:: 661
487:ISSN
448:ISBN
408:ISSN
38:, a
477:doi
400:doi
354:171
250:or
214:of
56:arc
34:In
910::
495:MR
493:,
485:,
473:45
471:,
465:,
446:.
424:MR
422:,
414:,
406:,
396:49
384:;
371:MR
365:,
190:.
80:.
528:e
521:t
514:v
479::
456:.
402::
299:3
294:R
263:3
259:S
236:3
231:R
176:3
172:S
146:3
141:R
116:]
113:1
110:,
107:0
104:[
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
