Making group topologies with, and without, convergent sequences

• Comfort, W.W. ^[1] ; Raczkowski, S.U. ^[2] ; Trigos-Arrieta, F.J. ^[2]
  1. [1] Wesleyan University

     Wesleyan University

     Town of Middletown, Estados Unidos

     
  2. [2] California State University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 7, Nº. 1, 2006, págs. 109-124
• Idioma: inglés
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• Resumen

  • (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.