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Proceedings of the American Mathematical Society
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
MathSciNet review: 640247
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0640247-1
PII: S 0002-9939(1982)0640247-1
Keywords: Tree, contractibility, topological semigroup
Article copyright: © Copyright 1982 American Mathematical Society