RT Journal Article
T1 Completeness properties of group topologies for R
A1 Martín Peinador, Elena
A1 Stevens, T. Christine
AB We study the completeness properties of several different group topologies for the additive group of real numbers, and we also compute the corresponding dual groups. We first present two metrizable connected group topologies on R with topologically isomorphic dual groups, one of which is noncomplete and arcwise connected and the other one is compact (therefore complete), but not arcwise connected. Using a theorem about T  -sequences and adapting a result about weakened analytic groups, we then describe a method for obtaining Hausdorff group topologies R that are strictly weaker than the usual topology and are complete. They are not Baire, and consequently not metrizable.
PB Elsevier Science
SN 0166-8641
YR 2015
FD 2015-09-01
LK https://hdl.handle.net/20.500.14352/24154
UL https://hdl.handle.net/20.500.14352/24154
LA eng
DS Docta Complutense
RD 3 may 2024