A duality between spheres and spheres with arcs
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- by Carl D. Sikkema
- Proc. Amer. Math. Soc. 25 (1970), 781-785
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259877-6
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Abstract:
The purpose of this paper is to extend the authors duality between nearly tame spheres and nearly tame arcs to a duality between wild spheres and tame spheres with nearly tame arcs properly attached, one arc for each wild point of the wild sphere.References
- B. J. Ball, The sum of two solid horned spheres, Ann. of Math. (2) 69 (1959), 253β257. MR 101511, DOI 10.2307/1970180
- R. H. Bing, Upper semicontinuous decompositions of $E^3$, Ann. of Math. (2) 65 (1957), 363β374. MR 92960, DOI 10.2307/1969968
- Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979β990. MR 27512, DOI 10.2307/1969408 N. Hosay, The sum of a cube and a crumpled cube is ${S^3}$, Abstract #607-17, Notices Amer. Math. Soc. 10 (1963), 666.
- Lloyd L. Lininger, Some results on crumpled cubes, Trans. Amer. Math. Soc. 118 (1965), 534β549. MR 178460, DOI 10.1090/S0002-9947-1965-0178460-7
- Joseph Martin, The sum of two crumpled cubes, Michigan Math. J. 13 (1966), 147β151. MR 190914
- Carl D. Sikkema, A duality between certain spheres and arcs in $S^{3}$, Trans. Amer. Math. Soc. 122 (1966), 399β415. MR 199851, DOI 10.1090/S0002-9947-1966-0199851-5
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 781-785
- MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259877-6
- MathSciNet review: 0259877