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 (1:221b)****[2]**R. H. Bing and J. M. Kister,*Taming complexes in hyperplanes*, Duke Math. J.**31**(1964), 491-511. MR**0164329 (29:1626)****[3]**S. Claytor,*Topological immersion of Peanian continua in a spherical surface*, Ann. of Math. (2)**35**(1934), 809-835. 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), 252-265. MR**1501343****[5]**J. M. Kister, ``Questions on isotopies in manifolds'' in*Topology of*3-*manifolds and related topics*, Prentice-Hall, Englewood Cliffs, N. J., 1962, pp. 229-230. 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*2-*space are isotopic in*3-*space*, 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), 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