In, Mane proved that if a compact metric space X admits an expansive homeomorphism, then X is finite dimensional. In, we introduced the notion of continuum-wise (fully) expansive homeomorphism and investigated the several properties. The class of continuum-wise expansive homeomorphisms is much larger than the class of expansive homeomorphisms. In relation to dimension theory, the following results were proved; (1) if a compact metric space X admits a continuum-wise expansive homeomorphism, then X is finite dimensional, and (2) if a continuum X admits a positively continuum-wise fully expansive map, then X is 1-dimensional .
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