Pseudo-arcs and connectedness in homeomorphism groups

Lewis, Wayne

doi:10.1090/S0002-9939-1983-0687655-1

Pseudo-arcs and connectedness in homeomorphism groups
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by Wayne Lewis

Proc. Amer. Math. Soc. 87 (1983), 745-748

DOI: https://doi.org/10.1090/S0002-9939-1983-0687655-1

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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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