Pacific Journal of Mathematics

Locally invariant topologies on free groups.

Sidney A. Morris and Peter Nickolas

Article information

Source
Pacific J. Math., Volume 103, Number 2 (1982), 523-537.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102723981

Mathematical Reviews number (MathSciNet)
MR705248

Zentralblatt MATH identifier
0525.22003

Subjects
Primary: 22A05: Structure of general topological groups
Secondary: 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)

Citation

Morris, Sidney A.; Nickolas, Peter. Locally invariant topologies on free groups. Pacific J. Math. 103 (1982), no. 2, 523--537. https://projecteuclid.org/euclid.pjm/1102723981


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References

  • [1] K. Bicknell and S. A. Morris, Norms on free topologcal groups, Bull. London Math. Soc, 10 (1978), 280-284.
  • [2] R. Brown and S. A. Morris, Embeddings in contractible or compact objects, Colloq. Math., 38 (1978), 213-222.
  • [3] T. H. Fay and B. V. Smith-Thomas, Free topological groups are almost never locally invariant,preprint.
  • [4] M. I. Graev, Free topological groups, Izv. Akad. Nauk. SSSR. Ser. Mat., 12 (1948), 279-324 (Russian); English translation in Amer. Math. Soc. Transl., 35 (1951); reprinted in Amer. Math. Soc. Transl., 8 (1962), 305-364.
  • [5] M. S. Khan, S. A. Morris and P. Niekolas, Local invarianceof free topological groups, to appear.
  • [6] S. A. Morris and Peter Nickolas, The extension of norms on subgroups of free topological groups, Proc. Amer. Math. Soc, 80 (1980), 185-188.
  • [7] S. A. Morris and H. B. Thompson, Invariantmetrics on free topological groups, Bull. Austral. Math. Soc, 9 (1973), 83-88.
  • [8] S. Swierczkowski, Topologies in free algebras, Proc London Math. Soc, (3) 14 (1964), 566-576.
  • [9] W. Taylor, Varieties obeying homotopy laws, Canad. J. Math., 29 (1977), 498-527.
  • [10] B. V. S. Thomas, Free topological groups, Gen. Top. and Appl., 4 (1974), 51-72.
  • [11] H. B. Thompson, Remarks on free topological groups with no small subgroups, J. Anstral. Math. Soc, 18 (1974), 482-484.