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Locally invariant topologies on free groups.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Morris, Sidney A. Nickolas, Peter |
| Copyright Year | 1982 |
| Abstract | In 1948, M. I. Graev proved that the free topological group on a completely regular Hausdorff space is Hausdorff, by showing that the free group admits a certain locally invariant Hausdorff group topology. In 1964, S. Swierczkowski gave a different proof, which also depends on the construction of a locally invariant topology. Yet another such construction follows from work of K. Bicknell and S. A. Morris. Graev's topology has proved to be essential in the investigation of free products of topological groups; Swierczkowski's topology is the key to the work of W. Taylor on varieties and homotopy laws; and Bicknell and Morris extend results of Abels on norms on free topological groups. In this paper, the three topologies are investigated in detail. It is seen that the Graev topology contains the Swierczkowski topology, which in turn contains that of Bicknell and Morris. These containments are shown to be proper in general. It is known that the topology of the free topological group is in general finer than each of these three topologies. |
| Starting Page | 523 |
| Ending Page | 537 |
| Page Count | 15 |
| File Format | PDF HTM / HTML |
| DOI | 10.2140/pjm.1982.103.523 |
| Alternate Webpage(s) | https://msp.org/pjm/1982/103-2/pjm-v103-n2-p23-s.pdf |
| Alternate Webpage(s) | https://doi.org/10.2140/pjm.1982.103.523 |
| Volume Number | 103 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
