Cellular subsets of the $3$-sphere
HTML articles powered by AMS MathViewer
- by D. G. Stewart
- Trans. Amer. Math. Soc. 114 (1965), 10-22
- DOI: https://doi.org/10.1090/S0002-9947-1965-0173244-8
- PDF | Request permission
References
- J. W. Alexander, On the subdivision of three space by a polyhedron, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 6-8.
- W. R. Alford and B. J. Ball, Some almost polyhedral wild arcs, Duke Math. J. 30 (1963), 33–38. MR 144312
- R. H. Bing, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 465–483. MR 87090
- R. H. Bing, Necessary and sufficient conditions that a $3$-manifold be $S^{3}$, Ann. of Math. (2) 68 (1958), 17–37. MR 95471, DOI 10.2307/1970041
- 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
- Morton Brown, The monotone union of open $n$-cells is an open $n$-cell, Proc. Amer. Math. Soc. 12 (1961), 812–814. MR 126835, DOI 10.1090/S0002-9939-1961-0126835-6
- Morton Brown and Herman Gluck, Stable structures on manifolds, Bull. Amer. Math. Soc. 69 (1963), 51–58. MR 145497, DOI 10.1090/S0002-9904-1963-10855-1
- Ralph H. Fox and Emil Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. (2) 49 (1948), 979–990. MR 27512, DOI 10.2307/1969408
- W. Graeub, Die semilinearen Abbildungen, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1950 (1950), 205–272 (German). MR 0042709
- O. G. Harrold Jr., The enclosing of simple arcs and curves by polyhedra, Duke Math. J. 21 (1954), 615–621. MR 68208
- O. G. Harrold Jr., Some consequences of the approximation theorem of Bing, Proc. Amer. Math. Soc. 8 (1957), 204–206. MR 87091, DOI 10.1090/S0002-9939-1957-0087091-X
- O. G. Harrold Jr. and E. E. Moise, Almost locally polyhedral spheres, Ann. of Math. (2) 57 (1953), 575–578. MR 53504, DOI 10.2307/1969738 H. Seifert and W. Threlfall, Lehrbuch der Topologie, Chelsea, New York, 1947.
- James F. Wardwell, Continuous Transformations Preserving all Topological Properties, Amer. J. Math. 58 (1936), no. 4, 709–726. MR 1507194, DOI 10.2307/2371242
Bibliographic Information
- © Copyright 1965 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 114 (1965), 10-22
- MSC: Primary 54.78
- DOI: https://doi.org/10.1090/S0002-9947-1965-0173244-8
- MathSciNet review: 0173244