The nonexistence of expansive homeomorphisms of 1-dimensional compact ANRs

Kato, Hisao

doi:10.1090/S0002-9939-1990-0991698-1

The nonexistence of expansive homeomorphisms of $1$-dimensional compact ANRs
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by Hisao Kato PDF

Proc. Amer. Math. Soc. 108 (1990), 267-269 Request permission

Abstract:

It is well known that if $X$ is an arc or a circle, then there is no expansive homeomorphism on $X$ (see [2] and [3]). In this note, we show that if $X$ is a Peano continuum which has a neighborhood $M$ such that ${\text {cl}}\left ( M \right )$ is a $1$-dimensional AR, then there is no expansive homeomorphism on $X$ . In particular, no $1$-dimensional compact ANR admits an expansive homeomorphism.

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