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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The extension of norms on subgroups of free topological groups


Authors: Sidney A. Morris and Peter Nickolas
Journal: Proc. Amer. Math. Soc. 80 (1980), 185-188
MSC: Primary 22A05
DOI: https://doi.org/10.1090/S0002-9939-1980-0574533-9
MathSciNet review: 574533
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Abstract: A norm on a group G is a nonnegative real-valued function N which is zero at the identity and satisfies $ N(x{y^{ - 1}}) \leqslant N(x) + N(y)$, for $ x,y \in G$. Let $ F(X)$ be the free topological group on a space X. Bicknell and Morris have shown that any norm on a subgroup of $ F(X)$ generated by a finite subset of X may be extended to a continuous norm on the whole of $ F(X)$. In this note a very direct and simple proof of this theorem is given.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0574533-9
Keywords: Norm on a topological group, free topological group
Article copyright: © Copyright 1980 American Mathematical Society

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