"On entropies in quasi-metric spaces"Olela-Otafudu, OlivierQuasi-uniform entropy $h_{QU}(\psi)$ is defined for a uniformly continuous self-map $\psi$ on a quasi-metric space $(X,q)$. General statements are proved about this entropy, and it is shown that the quasi-uniform entropy $h_{QU}(\psi ,q)$ is less or equals to the uniform entropy $h_U(\psi, q^s)$ for a uniformly continuous self-map $\psi$ on a quasi-metric space $(X,q)$. Finally we proved that the completion theorem for quasi-uniform entropy holds in the class of all join-compact quasi-metric spaces. |
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