query: Open subgroups of $\mathbb{R}$
positive_passages.docid: 152825
positive_passages.text: what are all the open subgroups of $(\mathbb{R},+)$
negative_passages.docid: 151705
negative_passages.text: $SL_n(\mathbb R)$ is a subgroup of kernel of $f\in$ Hom$(GL_n(\mathbb R), A)$, $A$ is an abelian group.
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 85175
negative_passages.text: Continuous Images of $GL_n(\mathbb{R})$
negative_passages.docid: 49220
negative_passages.text: Open Sets of $\mathbb{R}^1$ and axiom of choice
negative_passages.docid: 75068
negative_passages.text: subgroups of $\mathbb Z / 2 \mathbb Z \times \mathbb Z / 2 \mathbb Z$
negative_passages.docid: 56728
negative_passages.text: Question about limit points of a Subset of $\mathbb{R}$
negative_passages.docid: 128730
negative_passages.text: Open subspaces of locally compact Hausdorff spaces are locally compact
negative_passages.docid: 142228
negative_passages.text: Proof that a subset closed under group operation of a finite group is a subgroup
negative_passages.docid: 153797
negative_passages.text: Is a quotient group a subgroup?
negative_passages.docid: 97928
negative_passages.text: Normal subgroup of a normal subgroup
negative_passages.docid: 94825
negative_passages.text: Open set as a finite union of closed sets
negative_passages.docid: 138297
negative_passages.text: Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
negative_passages.docid: 138202
negative_passages.text: Every open set in $\mathbb{R}$ is a countable union of closed sets
negative_passages.docid: 10602
negative_passages.text: Monotone Union of subgroups being subgroup
negative_passages.docid: 33309
negative_passages.text: Subgroup of $\mathbb{R}$ either dense or has a least positive element?
negative_passages.docid: 129943
negative_passages.text: Torsion on $\pi_1(X)$, $X$ connected and open in $\mathbb{R}^n$