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Invariant metrics on free topological groups
| Content Provider | Scilit |
|---|---|
| Author | Morris, Sidney A. Thompson, H. B. |
| Copyright Year | 1973 |
| Description | For a completely regular space X, G(X) denotes the free topological group on X in the sense of Graev. Graev proves the existence of G(X) by showing that every pseudo-metric on X can be extended to a two-sided invariant pseudo-metric on the abstract group G(X). It is natural to ask if the topology given by these two-sided invariant pseudo-metrics on G(X) is precisely the free topological group topology on G(X). If X has the discrete topology the answer is clearly in the affirmative. It is shown here that if X is not totally disconnected then the answer is always in the negative. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4ABF78B84AEA6141E894410C37B9A382/S0004972700042908a.pdf/div-class-title-invariant-metrics-on-free-topological-groups-div.pdf |
| Ending Page | 88 |
| Page Count | 6 |
| Starting Page | 83 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700042908 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 9 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1973-08-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Applied Mathematics Free Topological Group |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
