Making group topologies with, and without, convergent sequences


  • W. W. Comfort Wesleyan University
  • S. U. Raczkowski California State University
  • F. J. Trigos-Arrieta California State University



Haar measure, Dual group, Character, Pseudocompact group, Totally bounded group, Maximal topology, Convergent sequence, Torsion-free group, Torsion group, Torsion-free rank, p-rank, p-adic integers


(1) Every infinite, Abelian compact (Hausdorff) group K admits 2|K|- many dense, non-Haar-measurable subgroups of cardinality |K|. When K is nonmetrizable, these may be chosen to be pseudocompact.

(2) Every infinite Abelian group G admits a family A of 22|G|-many pairwise nonhomeomorphic totally bounded group topologies such that no nontrivial sequence in G converges in any of the topologies T ϵ A. (For some G one may arrange ω(G, T ) < 2|G| for some T ϵ A.)

(3) Every infinite Abelian group G admits a family B of 22|G|-many pairwise nonhomeomorphic totally bounded group topologies, with ω (G, T ) = 2|G| for all T ϵ B, such that some fixed faithfully indexed sequence in G converges to 0G in each T ϵ B.


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Author Biographies

W. W. Comfort, Wesleyan University

Department of Mathematics

S. U. Raczkowski, California State University

Department of Mathematics

F. J. Trigos-Arrieta, California State University

Department of Mathematics


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How to Cite

W. W. Comfort, S. U. Raczkowski, and F. J. Trigos-Arrieta, “Making group topologies with, and without, convergent sequences”, Appl. Gen. Topol., vol. 7, no. 1, pp. 109–124, Apr. 2006.



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