On convergence groups with dense coarse subgroups

Dikran N. Dikranjan; Roman Frič; Fabio Zanolin

Czechoslovak Mathematical Journal (1987)

  • Volume: 37, Issue: 3, page 471-479
  • ISSN: 0011-4642

How to cite

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Dikranjan, Dikran N., Frič, Roman, and Zanolin, Fabio. "On convergence groups with dense coarse subgroups." Czechoslovak Mathematical Journal 37.3 (1987): 471-479. <http://eudml.org/doc/13655>.

@article{Dikranjan1987,
author = {Dikranjan, Dikran N., Frič, Roman, Zanolin, Fabio},
journal = {Czechoslovak Mathematical Journal},
keywords = {precompact group; convergence structure; topological groups; coarse convergence groups; sequentially compact; divisible Abelian group},
language = {eng},
number = {3},
pages = {471-479},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On convergence groups with dense coarse subgroups},
url = {http://eudml.org/doc/13655},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Dikranjan, Dikran N.
AU - Frič, Roman
AU - Zanolin, Fabio
TI - On convergence groups with dense coarse subgroups
JO - Czechoslovak Mathematical Journal
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 3
SP - 471
EP - 479
LA - eng
KW - precompact group; convergence structure; topological groups; coarse convergence groups; sequentially compact; divisible Abelian group
UR - http://eudml.org/doc/13655
ER -

References

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  1. D. Dikranjan, Sur la minimalité dies produits de groupes topologiques abéliens, C.R. Acad. Sc. Paris t. 299, Série I, No. 8 (1984), 303-306. (1984) Zbl0565.22002MR0761252
  2. R. Frič, F. Zanolin, Remarks on sequential convergence in free groups, Colloq. Math. Soc. János Bollyai, 41. Topology and Applications, Eger (Hungary), 1983, North-Holland, Amsterdam, 1985, 283-291. (1983) Zbl0618.22001MR0863910
  3. R. Frič, F. Zanolin, Coarse convergence groups, Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyně 1984). Akademie-Verlag Berlin, 1985, 107-114. (1984) Zbl0589.54003MR0835476
  4. R. Frič, P. Vojtáš, Diagonal conditions in sequential convergence, Convergence Structures 1984 (Proc. Conf. on Convergence, Bechyně 1984). Akademie-Verlag Berlin, 1985, 77-94. (1984) Zbl0601.54025MR0835474
  5. L. Fuchs, Infinite abelian groups I, II, Academic Press, New York 1970, 1973. (1970) Zbl0209.05503
  6. J. Jakubík, On convergence in linear spaces, (Slovak. Russian summary.) Mat.-Fyz. Časopis Sloven. Akad. Vied 6 (1956), 57-67. (1956) MR0084718
  7. V. Koutník, Completeness of sequential convergence groups, Studia Math. 77 (1983), 455-464. (1983) Zbl0546.54006MR0751766
  8. J. Novák, On some problems concerning the convergence spaces and groups, General Topology and its Relations to Modern Analysis and Algebra (Proc. Kanpur Topological Conf., 1968), Academia, Praha 1970, 219-229. (1968) MR0278253
  9. J. Novák, On convergence groups, Czechoslovak Math. J. 20 (1970), 357-374. (1970) Zbl0217.08504MR0263973
  10. J. Novák, On completions of convergence commutative groups. General Topology and its Relations to Modern Analysis and Algebra III, (Proc. Third Prague Topological Sympos., 1971), Academia, Praha 1972, 335-340. (1971) MR0365451
  11. I. Prodanov, Precompact minimal group topologies and p-adic numbers, Annuaire Univ. Sofia Fac. Math. 66 (1971/1972), 249-266. (1971) Zbl0329.22002MR0412323
  12. R. Stephenson, 10.1007/BF02052870, Math. Ann. 142 (1971), 193-195. (1971) Zbl0206.31601MR0286934DOI10.1007/BF02052870
  13. F. Zanolin, Solution of a problem of Josef Novák about convergence groups, Boll. Un. Mat. Ital., (5) 14-A (1977), 375-381. (1977) Zbl0352.54017MR0451220
  14. F. Zanolin, Example of a convergence commutative group which is not separated, Czechoslovak Math. J. 34 (1984), 169-171. (1984) Zbl0546.54007MR0743481

Citations in EuDML Documents

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  1. Roman Frič, Rationals with exotic convergences. II.
  2. Roman Frič, Products of coarse convergence groups
  3. Roman Frič, Fabio Zanolin, Coarse sequential convergence in groups, etc
  4. Ján Jakubík, Sequential convergences in distributive lattices
  5. Petr Simon, Rationals as a non-trivial complete convergence group
  6. Matúš Harminc, Ján Jakubík, Maximal convergences and minimal proper convergences in -groups
  7. Roman Frič, János Gerlits, On the sequential order
  8. Roman Frič, Fabio Zanolin, Relatively coarse sequential convergence
  9. Roman Frič, Rationals with exotic convergences

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