Piercing points on a special arc
HTML articles powered by AMS MathViewer
- by Harvey Rosen PDF
- Proc. Amer. Math. Soc. 46 (1974), 438-442 Request permission
Abstract:
We describe a cellular wild arc $A$ in ${S^3}$ that is the closure of the union of a null sequence of Alford arcs and show that if $S$ is an arbitrary $2$-sphere containing $A$ and tame modulo $A$, then each point of $A$ is a piercing point of $S$.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
- 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
- C. E. Burgess and J. W. Cannon, Embeddings of surfaces in $E^{3}$, Rocky Mountain J. Math. 1 (1971), no. 2, 259–344. MR 278277, DOI 10.1216/RMJ-1971-1-2-259
- J. C. Cantrell, Almost locally polyhedral $2$-spheres in $S^{3}$, Duke Math. J. 30 (1963), 249–252. MR 148042
- Robert J. Daverman and William T. Eaton, Universal crumpled cubes, Topology 11 (1972), 141–146. MR 292048, DOI 10.1016/0040-9383(72)90009-2
- 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
- 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
- D. R. McMillan Jr., Some topological properties of piercing points, Pacific J. Math. 22 (1967), 313–322. MR 216486
- 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
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 438-442
- MSC: Primary 55A30
- DOI: https://doi.org/10.1090/S0002-9939-1974-0356025-2
- MathSciNet review: 0356025