Homeomorphic continuous curves in -space are isotopic in -space.

Author:
W. K. Mason

Journal:
Trans. Amer. Math. Soc. **142** (1969), 269-290

MSC:
Primary 54.78

DOI:
https://doi.org/10.1090/S0002-9947-1969-0246276-2

MathSciNet review:
0246276

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References | Similar Articles | Additional Information

**[1]**V. W. Adkisson and Saunders MacLane,*Extending maps of plane Peano continua*, Duke Math. J.**6**(1940), 216–228. MR**0001345****[2]**R. H. Bing and J. M. Kister,*Taming complexes in hyperplanes*, Duke Math. J.**31**(1964), 491–511. MR**0164329****[3]**Schieffelin Claytor,*Topological immersion of Peanian continua in a spherical surface*, Ann. of Math. (2)**35**(1934), no. 4, 809–835. MR**1503198**, https://doi.org/10.2307/1968496**[4]**Harry Merrill Gehman,*On extending a continuous (1-1) correspondence of two plane continuous curves to a correspondence of their planes*, Trans. Amer. Math. Soc.**28**(1926), no. 2, 252–265. MR**1501343**, https://doi.org/10.1090/S0002-9947-1926-1501343-X**[5]**J. M. Kister,*Questions on isotopies in manifolds*, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 229–230. MR**0140106****[6]**V. L. Klee Jr.,*Some topological properties of convex sets*, Trans. Amer. Math. Soc.**78**(1955), 30–45. MR**0069388**, https://doi.org/10.1090/S0002-9947-1955-0069388-5**[7]**W. K. Mason,*Homeomorphic continuous curves in 2-space are isotopic in 3-space.*, Trans. Amer. Math. Soc.**142**(1969), 269–290. MR**0246276**, https://doi.org/10.1090/S0002-9947-1969-0246276-2**[8]**Robert L. Moore,*Concerning continuous curves in the plane*, Math. Z.**15**(1922), no. 1, 254–260. MR**1544571**, https://doi.org/10.1007/BF01494397**[9]**-,*Concerning the common boundary of two domains*, Fund. Math.**6**(1924), 212.**[10]**Gordon Thomas Whyburn,*Analytic Topology*, American Mathematical Society Colloquium Publications, v. 28, American Mathematical Society, New York, 1942. MR**0007095****[11]**R. L. Wilder,*Concerning continuous curves*, Fund. Math.**7**(1925), 340-377.**[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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DOI:
https://doi.org/10.1090/S0002-9947-1969-0246276-2

Article copyright:
© Copyright 1969
American Mathematical Society