query: Unit $d$-sphere looks locally like $\mathbb R^{d-1}\times\{0\}$ under a suitable diffeomorphism
positive_passages.docid: 152725
positive_passages.text: Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)
negative_passages.docid: 68234
negative_passages.text: Is $[0,1) \cup \{2\}$ a manifold with boundary? My issue is the $2$.
negative_passages.docid: 143043
negative_passages.text: When is a local homeomorphism a covering map?
negative_passages.docid: 92746
negative_passages.text: $\Delta \mathbf n = -2 \mathbf n$ on the Euclidean sphere
negative_passages.docid: 93471
negative_passages.text: Space of homeomorphisms Homeo$(S^1)$ of $S^1$ deformation retracts onto $O(2)$
negative_passages.docid: 146839
negative_passages.text: Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
negative_passages.docid: 151735
negative_passages.text: $\mathbb{R}^3 \setminus A$ deformation retracts onto $S^1 \vee S^2$
negative_passages.docid: 154837
negative_passages.text: mapping properties of $(1−z)^i$
negative_passages.docid: 56433
negative_passages.text: Volume form on $(n-1)$-sphere $S^{n-1}$
negative_passages.docid: 33969
negative_passages.text: "Basis extension theorem" for local smooth vector fields
negative_passages.docid: 44194
negative_passages.text: How to show that the unit sphere is a topological manifold?
negative_passages.docid: 113915
negative_passages.text: A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$
negative_passages.docid: 138563
negative_passages.text: If $f$ is ananlytic in $D_r(z_0)$\ {$z_0$} and $Ref(z)>0$ for all $z\in D_r(z_0)$\ {$z_0$} then $z_0$ is a removable singularity
negative_passages.docid: 97637
negative_passages.text: Showing that isotropy groups are submanifolds
negative_passages.docid: 151285
negative_passages.text: Existence of a local geodesic frame
negative_passages.docid: 82458
negative_passages.text: Homeomorphism between the unit disc and the unit square
negative_passages.docid: 84301
negative_passages.text: Showing that some Function on the Unit Disc is injective