About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Villegas-Silva, Luis Miguel
On resolvable spaces and groups. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 36 (1995), issue 3, pp. 579-584
MSC: 20K45, 22A05, 54D20, 54H11 | MR 1364498 | Zbl 0837.22001
Keywords:
resolvable; maximal; $\alpha$-bounded
Summary:
It is proved that every uncountable $\omega$-bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.
References:
[A] Anderson D.R.: On connected irresolvable Hausdorff spaces. Proc. Amer. Math. Soc. 16 (1965), 463-466. MR 0178443 | Zbl 0127.13003
[Be] Bell M.G.: On the combinatorial principle $P(c)$. Fund. Math. 114 (1981), 149-157. MR 0643555
[Bo] Booth D.: Ultrafilters on a countable set. Ann. Pure Appl. Logic (1970), 1-24. MR 0277371 | Zbl 0231.02067
[CF] Comfort W.W., Feng L.: The union of resolvable space is resolvable. preprint, 1993. MR 1221007
[CG] Comfort W.W., Garcí a-Ferreira S.: manuscript in preparation, 1900.
[CGvM] Comfort W.W., Gladdines H., Van Mill J.: Proper pseudocompact subgroups of pseudocompact Abelian groups. preprint, 1993. Zbl 0915.54029
[CvM] Comfort W.W., Van Mill J.: Groups with only resolvable topologies. preprint, 1993.
[CMZ] Comfort W.W., Masaveau O., Zhou H.: Resolvability in topology and in topological groups. Proc. Ninth (June 1993) Summer Topology Conference, Ann. New York Acad. Sci., to appear. MR 1462378
[GG] García-Ferreira S., García-Máynez A.: On weakly pseudocompact spaces. Houston J. Math. 20 (1994), 145-159. MR 1272568
[G] Guran I.I.: On topological groups close to being Lindelöf. Soviet Math. Dokl. 23 (1981), 173-175. Zbl 0478.22002
[H] Hewitt E.: A problem of set-theoretic topology. Duke Math. J. 10 (1943), 309-333. MR 0008692 | Zbl 0060.39407
[L] Louveau A.: Sur un article de S. Sirota. Bull. Sci. Math. (2) 96 (1972), 3-7. MR 0308326 | Zbl 0228.54032
[M] Malykhin V.I.: Extremally disconnected and similar groups. Soviet Math. Dokl. 16 (1975), 21-25. Zbl 0322.22003
[P] Padmavally K.: An example of a connected irresolvable Hausdorff spaces. Duke Math. J. 20 (1953), 513-520. MR 0059539
Partner of
EuDML logo