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1998 | 77 | 1 | 1-8
Tytuł artykułu

A relatively free topological group that is not varietal free

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
Rocznik
Tom
77
Numer
1
Strony
1-8
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-24
Twórcy
  • School of Mathematical and Computing Sciences, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand
  • Department of Mathematical Sciences, Faculty of Science, Ehime University, Matsuyama 790, Japan
Bibliografia
  • [1] A. V. Arhangel'skiĭ [A. V. Arkhangel'skiĭ], Any topological group is a quotient group of a zero-dimensional topological group, Soviet. Math. Dokl. 23 (1981), 615-618.
  • [2] A. V. Arhangel'skiĭ [A. V. Arkhangel'skiĭ], Classes of topological groups, Russian Math. Surveys 36 (1981), 151-174.
  • [3] M. S. Brooks, S. A. Morris and S. A. Saxon, Generating varieties of topological groups, Proc. Edinburgh Math. Soc. 18 (1973), 191-197.
  • [4] W. W. Comfort and J. van Mill, On the existence of free topological groups, Topology Appl. 29 (1988), 245-265.
  • [5] R. Engelking, General Topology, PWN, Warszawa, 1977.
  • [6] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, 2nd ed. Springer, 1979.
  • [7] K. H. Hofmann, An essay on free compact groups, in: Lecture Notes in Math. 915, Springer, 1982, 171-197.
  • [8] H. J. K. Junnila, Stratifiable pre-images of topological spaces, in: Topology (Budapest 1978), Colloq. Math. Soc. János Bolyai 23, North-Holland, 1980, 689-703.
  • [9] S. Mac Lane, Categories for the Working Mathematician, Grad. Texts in Math. 5, Springer, 1971.
  • [10] A. A. Markov, On free topological groups, Dokl. Akad. Nauk SSSR 31 (1941), 299-301 (in Russian).
  • [11] A. A. Markov, Three papers on topological groups, Amer. Math. Soc. Transl. 30 (1950), 120 pp.
  • [12] S. A. Morris, Varieties of topological groups, Bull. Austral. Math. Soc. 1 (1969), 145-160.
  • [13] S. A. Morris, Varieties of topological groups and left adjoint functor, J. Austral. Math. Soc. 16 (1973), 220-227.
  • [14] S. A. Morris, Varieties of topological groups. A survey, Colloq. Math. 46 (1982), 147-165.
  • [15] S. A. Morris, Free abelian topological groups, in: Categorical Topology (Toledo, Ohio, 1983), Heldermann, 1984, 375-391.
  • [16] H. Neumann, Varieties of Groups, Ergeb. Math. Grenzgeb. 37, Springer, Berlin, 1967.
  • [17] V. G. Pestov, Neighbourhoods of unity in free topological groups, Moscow Univ. Math. Bull. 40 (1985), 8-12.
  • [18] V. G. Pestov, Universal arrows to forgetful functors from categories of topological algebra, Bull. Austral. Math. Soc. 48 (1993), 209-249.
  • [19] P. Samuel, On universal mappings and free topological groups, Bull. Amer. Math. Soc. 54 (1948), 591-598.
  • [20] D. B. Shakhmatov, Zerodimensionality of free topological groups and topological groups with noncoinciding dimensions, Bull. Polish Acad. Sci. Math. 37 (1989), 497-506.
  • [21] D. B. Shakhmatov, Imbeddings into topological groups preserving dimensions, Topology Appl. 36 (1990), 181-204.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv77z1p1bwm
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