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Metrizability of sequential topological groups with point-countable $k$-networks

Author: Alexander Shibakov
Journal: Proc. Amer. Math. Soc. 126 (1998), 943-947
MSC (1991): Primary 54H11; Secondary 54D55, 54A20, 54E35
MathSciNet review: 1443165
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Abstract: We prove that a Hausdorff sequential topological group with a point-countable $k$-network is metrizable iff its sequential order is less than $\omega _{1}$. In the non Hausdorff case metrizability may be replaced by $\sigma $-locally finite base.

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Additional Information

Alexander Shibakov
Affiliation: Department of Mathematics, Auburn University, Auburn University, Alabama 36849

Keywords: Topological group, sequential space, sequential order, Fr\'{e}chet space, $k$-network
Received by editor(s): May 10, 1995
Received by editor(s) in revised form: September 15, 1996
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1998 American Mathematical Society

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