On the length of chains of proper subgroups covering a topological group

Details On the length of chains of proper subgroups covering a topological group On the length of chains of proper subgroups covering a topological group

2010-11-03

arxiv.org/abs/1011.1031v1

Arch. Math. Logic 50:3-4 (2011), 411-421

Mathematics

Logic

Scientific paper

10.1007/s00153-010-0222-7

We prove that if an ultrafilter L is not coherent to a Q-point, then each analytic non-sigma-bounded topological group G admits an increasing chain of its proper subgroups such that: (i) U_{a in b(L)} G_a=G; and $(ii)$ For every sigma-bounded subgroup H of G there exists a such that H is a subset of G_a. In case of the group Sym(w) of all permutations of w with the topology inherited from w^w this improves upon earlier results of S. Thomas.

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