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arXiv · 1908.11620

APD profiles and transfinite asymptotic dimension

Kamil Orzechowski
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Abstract

We develop the theory of APD profiles introduced by J. Dydak for $\infty$-pseudometric spaces. We connect them with transfinite asymptotic dimension defined by T. Radul. We give a characterization of spaces with transfinite asymptotic dimension at most $\omega+n$ for $n\in\omega$ and a sufficient condition for a space to have transfinite asymptotic dimension at most $m\cdot \omega+n$ for $m,n\in\omega$, using the language of APD profiles.

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Kamil Orzechowski. 2019-08-30. APD profiles and transfinite asymptotic dimension. https://arxiv.org/abs/1908.11620

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