query: About the topology of the Heisenberg group
positive_passages.docid: 142795
positive_passages.text: Is "connected, simply connected" Redundant?
negative_passages.docid: 58135
negative_passages.text: Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$
negative_passages.docid: 58484
negative_passages.text: Is the topological product $\Pi \{G_\alpha: \alpha < \kappa\} $ a topological group?
negative_passages.docid: 95867
negative_passages.text: Subgroup of $C^*$ (nonzero complex) with finite index.
negative_passages.docid: 44194
negative_passages.text: How to show that the unit sphere is a topological manifold?
negative_passages.docid: 32428
negative_passages.text: Group homomorphisms and which of the following statements are true (NBHM-$2014$)
negative_passages.docid: 135126
negative_passages.text: Proving that the quotient manifold is orientable if and only if the group action is orientation-preserving
negative_passages.docid: 90092
negative_passages.text: Showing that $\bar{\mathbb{B}}^n$ is a manifold with boundary (Lee ITM Probelm 3-4)
negative_passages.docid: 55652
negative_passages.text: Fundamental group of the torus
negative_passages.docid: 150796
negative_passages.text: Subspace topology and order topology (2)
negative_passages.docid: 141190
negative_passages.text: Fundamental group of mapping torus?
negative_passages.docid: 16860
negative_passages.text: set of almost complex structures on $\mathbb R^4$ as two disjoint spheres
negative_passages.docid: 154682
negative_passages.text: G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
negative_passages.docid: 11015
negative_passages.text: Given a group $ G $, how many topological/Lie group structures does $ G $ have?
negative_passages.docid: 64993
negative_passages.text: Connectedness of the $S^2$ sphere
negative_passages.docid: 51871
negative_passages.text: Characterization of Topology
negative_passages.docid: 150987
negative_passages.text: Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent