Homeomorphic continuous curves in space are isotopic in space.
Author:
W. K. Mason
Journal:
Trans. Amer. Math. Soc. 142 (1969), 269290
MSC:
Primary 54.78
MathSciNet review:
0246276
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References 
Similar Articles 
Additional Information
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Summary of lectures and Seminars, Summer Institute on Set Theoretic Topology, Madison, Wisconsin, (1955, revised 1958); p. 57, Question 8.
 [1]
 V. W. Adkisson and Saunders MacLane, Extending maps of plane Peano continua, Duke Math. J. 6 (1940), 216228. MR 0001345 (1:221b)
 [2]
 R. H. Bing and J. M. Kister, Taming complexes in hyperplanes, Duke Math. J. 31 (1964), 491511. MR 0164329 (29:1626)
 [3]
 S. Claytor, Topological immersion of Peanian continua in a spherical surface, Ann. of Math. (2) 35 (1934), 809835. MR 1503198
 [4]
 H. M. Gehman, On extending a continuous  correspondence of two plane continuous curves to a correspondence of their planes, Trans. Amer. Math. Soc. 28 (1926), 252265. MR 1501343
 [5]
 J. M. Kister, ``Questions on isotopies in manifolds'' in Topology of 3manifolds and related topics, PrenticeHall, Englewood Cliffs, N. J., 1962, pp. 229230. MR 0140106 (25:3529)
 [6]
 V. L. Klee, Jr., Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 36. MR 0069388 (16:1030c)
 [7]
 W. K. Mason, Homeomorphic continuous curves in 2space are isotopic in 3space, Thesis, Univ. of Wisconsin, Madison, 1968. MR 0246276 (39:7580)
 [8]
 R. L. Moore, Concerning continuous curves in the plane, Math. Z. 15 (1922), 259. MR 1544571
 [9]
 , Concerning the common boundary of two domains, Fund. Math. 6 (1924), 212.
 [10]
 G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., Vol. 28, Amer. Math. Soc., Providence, R. I., 1942; reprint 1967. MR 0007095 (4:86b)
 [11]
 R. L. Wilder, Concerning continuous curves, Fund. Math. 7 (1925), 340377.
 [12]
 Summary of lectures and Seminars, Summer Institute on Set Theoretic Topology, Madison, Wisconsin, (1955, revised 1958); p. 57, Question 8.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196902462762
PII:
S 00029947(1969)02462762
Article copyright:
© Copyright 1969
American Mathematical Society
