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On a paper by M.V.Ferrer, S.Hernandez and D.Shakhmatov "A countable free closed non-reflexive subgroup of Z^continuum", Proc.AMS 145(2017).
- Speaker(s)
- Roman Pol
- Affiliation
- University of Warsaw
- Date
- April 11, 2018, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar
An abelian topological group H is (Pontrjagin) reflexive if the natural homomorphism from H into the group H^^ of characters on the group of characters on H is a homeomorphism of H onto H^^ (as in the celebrated Pontrjagin duality theorem for LCA groups). All direct products Z^kappa of the additive group of integers Z are reflexive and it was an open question if this is also true for closed subgroups of Z^kappa. Ferrer, Hernandez and Shakhmatov described a closed countable non-reflexive subgroup of Z^continuum. We shall show that some results of Andreas Blass, Journ. Algebra 169(1994), combined with ideas of Ferrer, Hernandez and Shakhmatov, provide a closed countable non-reflexive group in Z^b (the cardinal number b, related to the partial order <* in N^N, in some models of ZFC, can be smaller than continuum).
