query: What is the exact definition of unknotted spanning arc?
positive_passages.docid: 157136
positive_passages.text: Why a special ball in $S^3$ is unique?
negative_passages.docid: 71997
negative_passages.text: Extruding along a path
negative_passages.docid: 91446
negative_passages.text: Average arc length of a uniformly distributed points
negative_passages.docid: 90184
negative_passages.text: Partition of circumference into $3k$ arcs
negative_passages.docid: 16231
negative_passages.text: Non-Uniform Scaling during UV unwrap. What is this?
negative_passages.docid: 157578
negative_passages.text: perfect map in topology
negative_passages.docid: 125713
negative_passages.text: How to justify unicyclic connected graphs formula?
negative_passages.docid: 59658
negative_passages.text: Are $\mathrm{arccot}(x)$ and $\arctan(1/x)$ the same function?
negative_passages.docid: 99060
negative_passages.text: Fiber from $S^1$ to $\mathbb{R} P^1$ that does not admit a section.
negative_passages.docid: 155060
negative_passages.text: Confusion about definition of manifold with boundary
negative_passages.docid: 38473
negative_passages.text: Checking whether a graph is planar
negative_passages.docid: 62766
negative_passages.text: Topological Manifolds & Covers
negative_passages.docid: 85332
negative_passages.text: Is $\mathbb{R}^4$ minus a line simply connected?
negative_passages.docid: 112607
negative_passages.text: Why is homology invariant under deformation retraction/homotopy equivalence?
negative_passages.docid: 106059
negative_passages.text: $[S]$ means linear span of S. Then $[S] = [[S]]$
negative_passages.docid: 50886
negative_passages.text: Two disjoint spanning trees, spanning subgraph with all even degrees
negative_passages.docid: 123430
negative_passages.text: Can a topological manifold be non-connected and each component with different dimension?