The extension of norms on subgroups of free topological groups
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- by Sidney A. Morris and Peter Nickolas PDF
- Proc. Amer. Math. Soc. 80 (1980), 185-188 Request permission
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.References
- Kevin Bicknell and Sidney A. Morris, Norms on free topological groups, Bull. London Math. Soc. 10 (1978), no. 3, 280–284. MR 519909, DOI 10.1112/blms/10.3.280
- Ronald Brown and Sidney A. Morris, Embeddings in contractible or compact objects, Colloq. Math. 38 (1977/78), no. 2, 213–222. MR 578534, DOI 10.4064/cm-38-2-213-222
- S. Hartman and Jan Mycielski, On the imbedding of topological groups into connected topological groups, Colloq. Math. 5 (1958), 167–169. MR 100044, DOI 10.4064/cm-5-2-167-169
- Sidney A. Morris, Varieties of topological groups, Bull. Austral. Math. Soc. 1 (1969), 145–160. MR 259010, DOI 10.1017/S0004972700041393
Additional Information
- © Copyright 1980 American Mathematical Society
- 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