query: Proving that $U(n)$ is a smooth manifold
positive_passages.docid: 157742
positive_passages.text: Prove that $U(n)$ is a manifold
negative_passages.docid: 152725
negative_passages.text: Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)
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: 27265
negative_passages.text: Continuously differentiable map from $\mathbb{R}^{m+n}$ to $\mathbb{R}^n$
negative_passages.docid: 65509
negative_passages.text: Several Questions on Smooth Urysohn's Lemma
negative_passages.docid: 99230
negative_passages.text: If a manifold M has zero Euler characteristic, there is a non-vanishing vector field on it
negative_passages.docid: 132063
negative_passages.text: locally on $S$ one of the coordinates is a $C^∞$ function of the other coordinate. Show that $S$ is a submanifold of $R^2$
negative_passages.docid: 63442
negative_passages.text: Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
negative_passages.docid: 21198
negative_passages.text: Proving that the general linear group is a differentiable manifold
negative_passages.docid: 64463
negative_passages.text: Proof that angle-preserving map is conformal
negative_passages.docid: 124861
negative_passages.text: The extension of smooth function
negative_passages.docid: 55089
negative_passages.text: Basis of the space of vector fields on smooth manifolds
negative_passages.docid: 108687
negative_passages.text: Open subsets in a manifold as submanifold of the same dimension?
negative_passages.docid: 149593
negative_passages.text: Global sections of a tensor product of vector bundles on a smooth manifold
negative_passages.docid: 107473
negative_passages.text: proof that on a compact manifold a vector field is complete
negative_passages.docid: 151637
negative_passages.text: How do we prove that this set is not manifold?
negative_passages.docid: 44955
negative_passages.text: Can $\mathbb CP^n$ be the boundary of a compact manifold?