Trees are contractible
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- by D. G. Paulowich PDF
- Proc. Amer. Math. Soc. 84 (1982), 429-432 Request permission
Abstract:
Any hereditarily unicoherent, locally connected, compact connected Hausdorff space is contractible using an ordered continuum. An example is given of a hereditarily unicoherent, locally connected, first countable, compact connected Hausdorff space that does not admit the structure of a topological semigroup with zero and identity.References
-
Carl Eberhart, Some classes of continua related to clan structures, dissertation, Louisiana State University, 1966.
- Karl Heinrich Hofmann and Paul S. Mostert, Elements of compact semigroups, Charles E. Merrill Books, Inc., Columbus, Ohio, 1966. MR 0209387
- R. J. Koch and L. F. McAuley, Semigroups on continua ruled by arcs, Fund. Math. 56 (1964), 1–8. MR 173240, DOI 10.4064/fm-56-1-1-8
- M. M. McWaters, Arcs, semigroups, and hyperspaces, Canadian J. Math. 20 (1968), 1207–1210. MR 231359, DOI 10.4153/CJM-1968-115-3
- Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4
- D. G. Paulowich, Weak contractibility and hyperspaces, Fund. Math. 94 (1977), no. 1, 41–47. MR 428253, DOI 10.4064/fm-94-1-35-39
- L. E. Ward Jr., Mobs, trees, and fixed points, Proc. Amer. Math. Soc. 8 (1957), 798–804. MR 97036, DOI 10.1090/S0002-9939-1957-0097036-4
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 429-432
- MSC: Primary 54F05; Secondary 54F50, 54F55
- DOI: https://doi.org/10.1090/S0002-9939-1982-0640247-1
- MathSciNet review: 640247