%0 Journal Article
%T Subgroups of the additive group of real line
%A Jitender Singh
%J Mathematics
%D 2013
%I arXiv
%X Without assuming the field structure on the additive group of real numbers $\mathbb{R}$ with the usual order $<,$ we explore the fact that every proper subgroup of $\mathbb{R}$ is either closed or dense. This property of subgroups of the additive group of reals is special and well known (see Abels and Monoussos [4]). However, by revisiting it, we provide another direct proof. We also generalize this result to arbitrary topological groups in the sense that, any topological group having this property of the subgroups in a given topology is either connected or totally disconnected.
%U http://arxiv.org/abs/1312.7067v3