On the supremum of the pseudocompact group topologies

Topology and its Applications

Volumn 155, Issue 4, 2008, Pages 213-224

  Comfort, W W ^a   van Mill, Jan ^b  

^a WESLEYAN UNIVERSITY   (United States)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Bohr topology; Precompact topological group; Pseudocompact topological group; Totally bounded topological group

Indexed keywords

EID: 37349000523     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2007.08.015     Document Type: Article

References (27)

1. Cater F.S., Erdo{combining double acute accent}s P., and Galvin F. On the density of λ-box products. General Topology Appl. 9 (1978) 307-312
2. Comfort W.W. Topological groups. In: Kunen K., and Vaughan J.E. (Eds). Handbook of Set-Theoretic Topology (1984), North-Holland, Amsterdam 1143-1263
3. Comfort W.W. On the "fragmentation" of certain pseudocompact groups. Bull. Greek Math. Soc. 25 (1984) 1-13
4. Comfort W.W., and Galindo J. Extremal pseudocompact topological groups. J. Pure Appl. Algebra 197 (2005) 59-81
5. Comfort W.W., and van Mill J. Concerning connected, pseudocompact Abelian groups. Topology Appl. 33 (1989) 21-45
6. Comfort W.W., and van Mill J. Extremal pseudocompact abelian groups are compact metrizable. Proc. Amer. Math. Soc. 135 (2007) 4039-4044
7. Comfort W.W., and Remus D. Imposing pseudocompact group topologies on Abelian groups. Fund. Math. 142 (1993) 221-240
8. Comfort W.W., and Remus D. Abelian torsion groups with a pseudocompact group topology. Forum Math. 6 (1994) 323-337
9. Comfort W.W., and Remus D. Pseudocompact refinements of compact group topologies. Math. Z. 215 (1994) 337-346
10. Comfort W.W., and Robertson L.C. Cardinality constraints for pseudocompact and for totally dense subgroups of compact Abelian groups. Pacific J. Math. 119 (1985) 265-285
11. Comfort W.W., and Robertson L.C. Extremal phenomena in certain classes of totally bounded groups. Dissertationes Math. (Rozprawy Mat.) vol. 272 (1988), Polish Scientific Publishers, Warszawa 48 p
12. Comfort W.W., and Ross K.A. Topologies induced by groups of characters. Fundamenta Math. 55 (1964) 283-291
13. Comfort W.W., and Ross K.A. Pseudocompactness and uniform continuity in topological groups. Pacific J. Math. 16 (1966) 483-496
14. Comfort W.W., and Saks V. Countably compact groups and finest totally bounded topologies. Pacific J. Math. 49 (1973) 33-44
15. Comfort W.W., and Soundararajan T. Pseudocompact group topologies and totally dense subgroups. Pacific J. Math. 100 (1982) 61-84
16. Dikranjan D.N., and Shakhmatov D.B. Pseudocompact topologizations of groups. Zb. Rad. Filoz. Fak. Nišu Ser. Mat. 4 (1990) 83-93
17. D.N. Dikranjan, D.B. Shakhmatov, Algebraic structure of the pseudocompact groups, Report 91-19, York University, Ontario, Canada, 1991, pp. 1-37
18. Dikranjan D.N., and Shakhmatov D.B. Algebraic structure of pseudocompact groups. Mem. Amer. Math. Soc. 133 (1998) 83 pages
19. van Douwen E.K. The weight of a pseudocompact (homogeneous) space whose cardinality has countable cofinality. Proc. Amer. Math. Soc. 80 (1980) 678-682
20. van Douwen E.K. The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G. Topology Appl. 34 (1990) 69-91
21. Fuchs L. Infinite Abelian Groups vol. I (1970), Academic Press, New York
22. Galindo J. Dense pseudocompact subgroups and finer pseudocompact group topologies. Sci. Math. Jpn. 55 (2002) 627-640
23. Gitik M., and Shelah S. On densities of box products. Topology Appl. 88 (1998) 219-237
24. Hewitt E. Rings of real-valued continuous functions I. Trans. Amer. Math. Soc. 64 (1948) 45-99
25. Hewitt E., and Ross K.A. Abstract Harmonic Analysis vol. I (1963), Springer-Verlag, Berlin
26. Itzkowitz G., and Shakhmatov D. Large families of dense pseudocompact subgroups of compact groups. Fund. Math. 147 (1995) 197-212
27. Weil A. Sur les Espaces à Structure Uniforme et sur la Topologie Générale. Publ. Math. Univ. Strasbourg vol. 551 (1938), Hermann & Cie, Paris