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On sequential analytic groups


Author: Alexander Y. Shibakov
Journal: Proc. Amer. Math. Soc. 145 (2017), 4087-4096
MSC (2010): Primary 54D55, 54H05; Secondary 54A20
DOI: https://doi.org/10.1090/proc/13514
Published electronically: March 27, 2017
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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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Additional Information

Alexander Y. Shibakov
Affiliation: Department of Mathematics, Tennessee Tech. University, 110 University Drive, Cookeville, Tennessee 38505
Email: ashibakov@tntech.edu

DOI: https://doi.org/10.1090/proc/13514
Keywords: Analytic space, topological group, sequential space
Received by editor(s): January 7, 2016
Received by editor(s) in revised form: January 19, 2016, January 21, 2016, and October 1, 2016
Published electronically: March 27, 2017
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2017 American Mathematical Society

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