Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Trees are contractible


Author: D. G. Paulowich
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Carl Eberhart, Some classes of continua related to clan structures, dissertation, Louisiana State University, 1966.
  • [2] K. H. Hofmann and P. S. Mostert, Elements of compact semigroups, Merrill, Columbus, 1966. MR 0209387 (35:285)
  • [3] R. J. Koch and L. F. McAuley, Semigroups on continua ruled by arcs, Fund. Math. 56 (1964), 1-8. MR 0173240 (30:3453)
  • [4] M. M. McWaters, Arcs, semigroups, and hyperspaces, Canad. J. Math. 20 (1968), 1207-1210. MR 0231359 (37:6914)
  • [5] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. MR 0042109 (13:54f)
  • [6] D. G. Paulowich, Weak contractibility and hyperspaces, Fund. Math. 94 ( 1977), 41-47. MR 0428253 (55:1278)
  • [7] L. E. Ward, Jr., Mobs, trees, and fixed points, Proc. Amer. Math. Soc. 8 (1957), 798-804. MR 0097036 (20:3516)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F05, 54F50, 54F55

Retrieve articles in all journals with MSC: 54F05, 54F50, 54F55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0640247-1
Keywords: Tree, contractibility, topological semigroup
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society