A problem of Martin concerning strongly convex metrics on $E^{3}$
HTML articles powered by AMS MathViewer
- by E. D. Tymchatyn and B. O. Friberg
- Proc. Amer. Math. Soc. 43 (1974), 461-464
- DOI: https://doi.org/10.1090/S0002-9939-1974-0336735-3
- PDF | Request permission
Abstract:
If $d$ is a strongly convex metric on ${E^3}$ and $C$ is a simple closed curve in ${E^3}$ such that $C$ is the union of three line segments then $C$ is unknotted.References
- R. H. Bing, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145β158. MR 61377, DOI 10.2307/1969836 Joseph Martin, Recent developments in the geometry of continuous curves, Topology Conference Arizona State University 1967, edited by E. E. Grace, Tempe, Arizona.
- Dale Rolfsen, Strongly convex metrics in cells, Bull. Amer. Math. Soc. 74 (1968), 171β175. MR 226591, DOI 10.1090/S0002-9904-1968-11926-3
- Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258, DOI 10.1515/9781400883875
- E. D. Tymchatyn, Antichains and products in partially ordered spaces, Trans. Amer. Math. Soc. 146 (1969), 511β520. MR 263037, DOI 10.1090/S0002-9947-1969-0263037-9 β, Some order theoretic characterizations of the $3$-cell, Colloq. Math. 24 (1972), 195-203.
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 461-464
- MSC: Primary 55A25
- DOI: https://doi.org/10.1090/S0002-9939-1974-0336735-3
- MathSciNet review: 0336735