Compactness type properties in topological groups

Mihail G. Tkachenko

Czechoslovak Mathematical Journal (1988)

  • Volume: 38, Issue: 2, page 324-341
  • ISSN: 0011-4642

How to cite

top

Tkachenko, Mihail G.. "Compactness type properties in topological groups." Czechoslovak Mathematical Journal 38.2 (1988): 324-341. <http://eudml.org/doc/13708>.

@article{Tkachenko1988,
author = {Tkachenko, Mihail G.},
journal = {Czechoslovak Mathematical Journal},
keywords = {bounded subset; countable spectrum of pseudocompact groups; open endomorphisms with pseudocompact kernels; inverse limit},
language = {eng},
number = {2},
pages = {324-341},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Compactness type properties in topological groups},
url = {http://eudml.org/doc/13708},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Tkachenko, Mihail G.
TI - Compactness type properties in topological groups
JO - Czechoslovak Mathematical Journal
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 2
SP - 324
EP - 341
LA - eng
KW - bounded subset; countable spectrum of pseudocompact groups; open endomorphisms with pseudocompact kernels; inverse limit
UR - http://eudml.org/doc/13708
ER -

References

top
  1. Arhangeľskii A. V., Topological spaces and continuous mappings. Notes on topological groups, - Moscow State University, 1969. (In Russian). (1969) 
  2. Arhangeľskii A. V., Cardinal invariants of topological groups. Imbeddings and condensations, - Soviet Math. Dokl., 1979, v. 20, N. 4, p. 783--787. (1979) MR0553825
  3. Arhangeľskii A. V., On linear homomorphisms of functional spaces, - Dokl. Acad. Sci. URSS, 1982, V. 264, N 6, p. 1286-1292. (In Russian). (1982) 
  4. Arhangeľskii A. V., Spaces of functions endowed with pointwise convergence topology and compact sets, - Uspekhy Math. Sci., 1984, v. 39, N 5, p. 11 - 50. (In Russian). (1984) MR0764007
  5. Blasco J. L., On μ -spaces and k R -spaces, - Proc. Amer. Math. Soc., 1977, v. 67, N 1, p. 179-186. (1977) MR0464152
  6. Chigogidze A. Ch., On χ -metrizable spaces, - Uspekhy Math. Sci., 1982, v. 37, N2, p. 241-242. (In Russian). (1982) MR0650791
  7. Comfort W. W., Ross K. A., Pseudocompactness and uniform continuity in topological groups, - Pacific J. Math., 1966, v. 16, N 3, pp. 483-496. (1966) Zbl0214.28502MR0207886
  8. Comfort W. W., Saks V., Countably compact groups and finest totally bounded uniformities, - Pacific J. Math., 1973, v. 49, N 1, p. 33-44. (1973) MR0372104
  9. Comfort W. W., Soundararajan T., Pseudocompact group topologies and totally dense subgroups, - Pacific J. Math., 1982, v. 100, N 1, p. 61-84. (1982) Zbl0451.22002MR0661441
  10. Comfort W. W., Robertson L. C., Extremal phenomena in certain classes of totally bounded groups, - Preprint. Zbl0703.22002MR0959432
  11. Douwen E. K. van, 10.1090/S0002-9947-1980-0586725-8, - Trans. Amer. Math. Soc., 1980, v. 262, N 2, p. 417-427. (1980) MR0586725DOI10.1090/S0002-9947-1980-0586725-8
  12. Engelking R., General Topology, - PWN, Warszawa, 1977. (1977) Zbl0373.54002MR0500780
  13. Grant G. L., Topological groups which satisfy an open mapping theorem, - Pacific J. Math., 1977, v. 68, N2, p. 411-423. (1977) Zbl0375.22002MR0466395
  14. Hajnal A., Juhász I., A separable normal topological group need not be Lindelöf, - Gen. Top. Appl., 1976, v. 6, p. 199-205. (1976) MR0431086
  15. Hewitt E., Ross K. A., Abstract harmonic analysis, vol. I, - Springer-Verlag, Berlin- Göttingen-Heidelberg, 1963. (1963) Zbl0115.10603MR0551496
  16. Matveev M. V., Pseudocompact spaces and spaces closed to being pseudocompact, - Dissertation, Moscow, 1984. (In Russian). (1984) 
  17. Noble N., Countably compact and pseudocompact products, - Czechoslovak Math. J., 1969, v. 19, N2, p. 390-397. (1969) Zbl0184.47706MR0248717
  18. Noble N, The continuity of functions on Cartesian products, - Trans. Amer. Math. Soc., 1970, v. 149, p, 187-198. (1970) Zbl0229.54028MR0257987
  19. Novák J., On the Cartesian product of two compact spaces, - Fund. Math., 1953, v. 40, p. 106-112. (1953) MR0060212
  20. Pontrjagin L. S., Continuous groups, - Moscow, 1973. (In Russian). (1973) MR0357673
  21. Roelcke W., Dierolf S., Uniform structures on topological groups and their quotients, -- N. Y., Mc Graw-Hill Inc., 1981. (1981) Zbl0489.22001MR0644485
  22. Tkačenko M. G., Some results on inverse spectra, II, - Comment. Math. Univ. Carol., 1981, V. 22, N4, p. 819-841. (1981) MR0647029
  23. Tkačenko M. G., 10.1007/BF01917540, - Acta Math. Acad. Sci. Hungar, 1981, v. 38, N 3, p. 257-261. (1981) MR0647345DOI10.1007/BF01917540
  24. Tkačenko M. G., Free topological groups and related topics, - Colloquia Math., 1983, v. 41, pp. 609-623. (1983) MR0863943
  25. Ščepin E. V., Topology of limit spaces of uncountable inverse spectra, - Uspekhy Math. Sci., 1976, V. 31, N 5, p. 191-226. (In Russian). (1976) MR0464137
  26. Ščepin E. V., Real-valued functions and canonical sets in Tychonoff products and topological groups, - Uspekhy Math. Sci., 1976, v. 31, N 6, p. 17-27. (In Russian). (1976) MR0458358
  27. Ščepin E. V., On χ -metrizable spaces, - Izv. Acad. Sec. URSS, 1979, v. 43, N 2, p. 442-478. (In Russian). (1979) MR0534603
  28. Uspenskiĭ V. V., On continuous images of Lindelöf topological groups, - Dokl. Acad. Sci. URSS, 1985, V. 285, N 4, p. 824-827. (In Russian). (1985) MR0821360

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.