Richeson, David, and Jim Wiseman. Positively Expansive Homeomorphisms of Compact Spaces. International Journal of Mathematics and Mathematical Sciences Volume 2004, Article ID 821324, 4 pp. https://doi.org/10.1155/S0161171204312184

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We give a new and elementary proof showing that a homeomorphism f:X→X of a compact metric space is positively expansive if and only if X is finite.