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APD profiles and transfinite asymptotic dimension (1908.11620v1)
Published 30 Aug 2019 in math.MG
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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