Making group topologies with, and without, convergent sequences
一般拓扑
2013-10-09 v1
摘要
(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 2^2^|G|-many pairwise nonhomeomorphic totally bounded group topologies such that no nontrivial sequence in G converges in any of the topologies T in A. (For some G one may arrange w(G,T) < 2^|G| for some T in A.) (3) Every infinite Abelian group admits a family B of 2^2^|G|-many pairwise nonhomeomorphic totally bounded group topologies, with w(G,T) = 2^|G| for all T in B, such that some fixed faithfully indexed sequence in G converges to 0_G in each T in B.
引用
@article{arxiv.math/0402443,
title = {Making group topologies with, and without, convergent sequences},
author = {W. W. Comfort and S. U. Raczkowski and F. J. Trigos-Arrieta},
journal= {arXiv preprint arXiv:math/0402443},
year = {2013}
}
备注
17 pages