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Total minimality of the unitary groups

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References

  1. Adian, S.: Classifications of periodic words and their application in group theory. In: Burnside Groups, Proc. Bielefeld, Germany 1977. Workshop, edited by J.L. Mennicke, pp. 1–40. Lecture Notes in Math., vol. 806. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  2. Antonjan, S., Smirnov, Yu.: Universal objects and bicompact extensions for topological groups of transformations. Dokl. Acad. Nauk SSSR257, 521–526 (1981) [Russian]. Engl. Transl.: Soviet Math. Dokl.23, 279–284 (1981)

    Google Scholar 

  3. Berberian, S.: Lectures in functional analysis and operator theory. Graduate texts in mathematics, vol. 15. New York-Heidelberg-Berlin: Springer 1974

    Google Scholar 

  4. Banaschewski, B.: Minimal topological algebras. Math. Ann.211, 107–114 (1974)

    Google Scholar 

  5. Bourbaki, N.: Topologie Generale. Paris: Hermann 1975

    Google Scholar 

  6. Comfort, W., Grant, L.: Cardinal invariants, pseudocompactness and minimality: some recent advances in the topological theory of topological groups. Topology Proc.6, 227–265 (1981)

    Google Scholar 

  7. Dierolf, S., Schwanengel, U.: Un example d'un groupe topologiqueq-minimaux mais non precompact. Bull. Sci. Math. (2)101, 265–269 (1977)

    Google Scholar 

  8. Dierolf, S., Schwanengel, U.: Examples of locally compact non-compact minimal tolological groups. Pacific J. Math.82, 349–355 (1979)

    Google Scholar 

  9. Dikranjan, D.: Minimal topologies on Abelian groups. Istituto di Algebra e Geometria de l'Università di Padova, 1983 (Preprint)

  10. Dikranjan, D., Prodanov, Iv.: Totally minimal topological groups. Annuaire Univ. Sofia Fac. Math. Méc.69, 5–11 (1974/75)

    Google Scholar 

  11. Eberhardt, V., Dierolf, S.: Produits d'espaces vectoriels topologiqueq-minimaux. C.R. Acad. Sci. Paris288, 275–277 (1979)

    Google Scholar 

  12. Eberhardt, V., Dierolf, S., Schwanengel, U.: On the product of two (totally) minimal topological groups and the three-space-problem. Math. Ann.251, 123–128 (1980)

    Google Scholar 

  13. Harpe, P. de la: Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space. Lecture Notes in Math., vol. 285. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  14. Hesse, G.: Zur Topologisierbarkeit von Gruppen. Dissertation, Hannover 1979

  15. Hewitt, E., Ross, K.: Abstract harmonic analysis I, Die Grundlehren der Mathematischen Wissenschaften, vol. 115. Berlin-Göttingen-Heidelberg: Springer 1963

    Google Scholar 

  16. Heyer, H.: Dualität lokalkompakter Gruppen. Lecture Notes in Math., vol. 150. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  17. Ludescher, H., Vries, J. de: A sufficient condition for the existence of aG-compactification. Indag. Math. (3)42, 263–268 (1980)

    Google Scholar 

  18. Prodanov, Iv.: Compact representations of continuous algebraic structures. General Topology and its Relations to Modern Analysis and Algebra II. Proc. of the Second Prague Topology Symposium, pp. 290–294 (1966) [Russian]. Prague: Academia 1967

    Google Scholar 

  19. Prodanov, Iv.: Some minimal group topologies are precompact. Math. Ann.227, 117–125 (1977)

    Google Scholar 

  20. Prodanov, Iv., Stojanov, L.: Every minimal Abelian group is precompact. C.R. Acad. Bulgare Sci.37, 23–26 (1984)

    Google Scholar 

  21. Schwanengel, U.: Minimale topologische Gruppen, Dissertation, München 1978

  22. Shelah, S.: On a problem of Kurosh, Jonsson groups and applications. In: Word Problems II (Adian, S.I., Boone, W.W., Higman, G., eds.), pp. 373–394. Amsterdam-London: North Holland 1980

    Google Scholar 

  23. Takesaki, M.: Theory of operator algebras I. Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  24. Vries, J. de: Topological transformation groups I. Amsterdam: Mathematical Centre 1975

    Google Scholar 

  25. Vries, J. de: Equivariant embeddings ofG-spaces. General Topology and its Relations to Modern Analysis and Algebra IV. Proc. of the Fourth Prague Top. Symposium, pp. 485–493 (1976)

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Stojanov, L. Total minimality of the unitary groups. Math Z 187, 273–283 (1984). https://doi.org/10.1007/BF01161710

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