On sequential analytic groups
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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.References
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Additional Information
- Alexander Y. Shibakov
- Affiliation: Department of Mathematics, Tennessee Tech. University, 110 University Drive, Cookeville, Tennessee 38505
- MR Author ID: 355084
- Email: ashibakov@tntech.edu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4087-4096
- MSC (2010): Primary 54D55, 54H05; Secondary 54A20
- DOI: https://doi.org/10.1090/proc/13514
- MathSciNet review: 3665059