Wild universally pierced arcs
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- by Harvey Rosen PDF
- Proc. Amer. Math. Soc. 58 (1976), 357-360 Request permission
Abstract:
We show that each arc in ${E^3}$ with two shrinking points is universally pierced. Examples of universally pierced arcs and a universally pierced simple closed curve are given.References
- W. R. Alford, Some “nice” wild $2$-spheres in $E^{3}$, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 29–33. MR 0141091
- R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 465–483. MR 87090
- Marston Morse, A reduction of the Schoenflies extension problem, Bull. Amer. Math. Soc. 66 (1960), 113–115. MR 117694, DOI 10.1090/S0002-9904-1960-10420-X
- J. W. Cannon, Characterization of taming sets on $2$-spheres, Trans. Amer. Math. Soc. 147 (1970), 289–299. MR 257996, DOI 10.1090/S0002-9947-1970-0257996-6
- P. H. Doyle and J. G. Hocking, Some results on tame disks and spheres in $E^{3}$, Proc. Amer. Math. Soc. 11 (1960), 832–836. MR 126839, DOI 10.1090/S0002-9939-1960-0126839-2
- David S. Gillman, Side approximation, missing an arc, Amer. J. Math. 85 (1963), 459–476. MR 160193, DOI 10.2307/2373136
- David S. Gillman, Sequentially $1-\textrm {ULC}$ tori, Trans. Amer. Math. Soc. 111 (1964), 449–456. MR 162234, DOI 10.1090/S0002-9947-1964-0162234-6
- O. G. Harrold Jr., H. C. Griffith, and E. E. Posey, A characterization of tame curves in three-space, Trans. Amer. Math. Soc. 79 (1955), 12–34. MR 91457, DOI 10.1090/S0002-9947-1955-0091457-4
- L. D. Loveland, Some universally pierced arcs in $E^{3}$, Proc. Amer. Math. Soc. 49 (1975), 469–474. MR 370590, DOI 10.1090/S0002-9939-1975-0370590-1
- D. R. McMillan Jr., Piercing a disk along a cellular set, Proc. Amer. Math. Soc. 19 (1968), 153–157. MR 220266, DOI 10.1090/S0002-9939-1968-0220266-2
- R. L. Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), no. 4, 416–428. MR 1501320, DOI 10.1090/S0002-9947-1925-1501320-8
- C. D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. (2) 66 (1957), 1–26. MR 90053, DOI 10.2307/1970113
- Harvey Rosen, Piercing points on a special arc, Proc. Amer. Math. Soc. 46 (1974), 438–442. MR 356025, DOI 10.1090/S0002-9939-1974-0356025-2
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 357-360
- MSC: Primary 57A10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0415621-6
- MathSciNet review: 0415621