query: Characterization of 1-dimensional manifolds.
positive_passages.docid: 22150
positive_passages.text: The only 1-manifolds are $\mathbb R$ and $S^1$
negative_passages.docid: 126136
negative_passages.text: Fundamental question about dimensional analysis
negative_passages.docid: 62766
negative_passages.text: Topological Manifolds & Covers
negative_passages.docid: 57740
negative_passages.text: Counting independent components of Riemann curvature tensor
negative_passages.docid: 91322
negative_passages.text: A diffeomorphism whose tangent map preserves dot products is an isometry.
negative_passages.docid: 89649
negative_passages.text: Linear Algebra munkres analysis on manifolds question.
negative_passages.docid: 91756
negative_passages.text: Degeneracy in one dimension
negative_passages.docid: 102323
negative_passages.text: Nice neighborhoods of each "piece" in a manifold connected sum
negative_passages.docid: 80100
negative_passages.text: Boundary of product manifolds such as $S^2 \times \mathbb R$
negative_passages.docid: 53809
negative_passages.text: Continuous map of differentiable manifolds is differentiable if differentiable functions pull back to differentiable functions
negative_passages.docid: 72602
negative_passages.text: Why is important for a manifold to have countable basis?
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)
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: 69798
negative_passages.text: Intersecting geodesics in a positive curvature manifold
negative_passages.docid: 141794
negative_passages.text: Invariant subspaces of specific dimension
negative_passages.docid: 71791
negative_passages.text: Smooth structure of embedded submanifolds
negative_passages.docid: 19453
negative_passages.text: Invariance of domain for manifold