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Proceedings of the American Mathematical Society

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

 

 

Semigroups on acyclic plane continua


Author: B. E. Wilder
Journal: Proc. Amer. Math. Soc. 28 (1971), 587-589
MSC: Primary 54.80
DOI: https://doi.org/10.1090/S0002-9939-1971-0276946-6
MathSciNet review: 0276946
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Abstract: It is shown that an acyclic irreducible plane continuum which admits the structure of a topological semigroup is an arc if it has an identity, and is either an arc, is trivial, or is decomposible into an arc if it satisfies $ {M^2} = M$. This extends some results of Friedberg and Mahavier concerning semigroups on chainable continua.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0276946-6
Keywords: Topological semigroup, clan, acyclic plane continua, arcwise connected
Article copyright: © Copyright 1971 American Mathematical Society