Ukrainian Mathematical Bulletin

Volume 4, Issue 3, 2007 pp. 429-431.

Discontinuous Birkhoff Theorem

Authors: O. Petrenko, Igor V. Protasov
Author institution: O. Petrenko, Igor V. Protasov, Department of Cybernetics, National T. Shevchenko University of Kyiv, Volodimirska 64, Kyiv, 01033, Ukraine protasov@unicyb.kiev.ua

Summary: A topological space $X$ is called totally recurrent if every mapping $f:X\rightarrow X$ has a recurrent point. We prove that a Hausdorff space $X$ is totally recurrent if and only if $X$ is either finite or a one-point compactification of an infinite discrete space.

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