On sequential analytic groups

Shibakov, Alexander

doi:10.1090/proc/13514

On sequential analytic groups
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by Alexander Y. Shibakov PDF

Proc. Amer. Math. Soc. 145 (2017), 4087-4096 Request permission

Abstract:

We answer a question of S. Todorčević and C. Uzcátegui from their 2005 work by showing that the only possible sequential orders of sequential analytic groups are $1$ and $\omega _1$. Other results on the structure of sequential analytic spaces and their relation to other classes of spaces are given as well. In particular, we provide a full topological classification of sequential analytic groups by showing that all such groups are either metrizable or $k_\omega$-spaces, which, together with a result by Zelenyuk, implies that there are exactly $\omega _1$ non-homeomorphic analytic sequential group topologies.

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