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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Pseudo-arcs and connectedness in homeomorphism groups


Author: Wayne Lewis
Journal: Proc. Amer. Math. Soc. 87 (1983), 745-748
MSC: Primary 54F20; Secondary 54F50, 54H15
MathSciNet review: 687655
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Abstract: We prove that the homeomorphism group of the pseudo-arc contains no nondegenerate continua. An equivalent result holds for any continuum all of whose small subcontinua are pseudo-arcs, e.g. for the pseudo-circle and the circle of pseudo-arcs. Related questions are briefly mentioned.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687655-1
PII: S 0002-9939(1983)0687655-1
Keywords: Continuum, pseudo-arc, homeomorphism group, homogeneity, hereditary indecomposability
Article copyright: © Copyright 1983 American Mathematical Society