A Note on Measure-Expansive Diffeomorphisms
Alfonso Artigue, Dante Carrasco-Olivera

TL;DR
This paper establishes the equivalence between countably-expansive and measure-expansive homeomorphisms and explores the implications for the structure of expansive diffeomorphisms in the $C^1$ topology.
Contribution
It proves the equivalence of countably-expansive and measure-expansive homeomorphisms and characterizes the $C^1$-interior of various expansive diffeomorphism sets.
Findings
Countably-expansive and measure-expansive homeomorphisms are equivalent.
The $C^1$-interior of expansive, measure-expansive, and continuum-wise expansive diffeomorphisms coincide.
Abstract
In this note we prove that a homeomorphism is countably-expansive if and only if it is measure-expansive. This result is applied for showing that the -interior of the sets of expansive, measure-expansive and continuum-wise expansive -diffeomorphisms coincide.
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