Trees are contractible

Paulowich, D. G.

doi:10.1090/S0002-9939-1982-0640247-1

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

Some classes of continua related to clan structures

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