query: $f$ extends to a smooth map $\tilde{f} : S^2 \to S^2$. - Is the proof legit?
positive_passages.docid: 21178
positive_passages.text: Show that $f$ extends to a smooth map.
negative_passages.docid: 23414
negative_passages.text: Topologist's Sine Curve: A rigorous proof of why $\overline{S} = S \cup V$
negative_passages.docid: 30178
negative_passages.text: Homeomorphism $(\mathbb{CP}^1)^m/S_m \overset{\sim}{\to} \mathbb{CP}^m$?
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: 33969
negative_passages.text: "Basis extension theorem" for local smooth vector fields
negative_passages.docid: 154496
negative_passages.text: Proving that the Hopf map $S^3 \to S^2$ is a submersion
negative_passages.docid: 96567
negative_passages.text: Immersion of $\mathbb{R}$ to $\mathbb{R}^2$
negative_passages.docid: 116732
negative_passages.text: Proving that a continuous map is surjective
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: 31747
negative_passages.text: Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space
negative_passages.docid: 64463
negative_passages.text: Proof that angle-preserving map is conformal
negative_passages.docid: 71037
negative_passages.text: Is exponential map locally a diffeomorphism w.r.t. base point?
negative_passages.docid: 22890
negative_passages.text: Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
negative_passages.docid: 19245
negative_passages.text: Schwartz Distribution Theory: (Non-)Surjectivity of $f \mapsto f*f$ in $ \mathcal E '$
negative_passages.docid: 118622
negative_passages.text: Local diffeomorphism from $\mathbb R^2$ onto $S^2$
negative_passages.docid: 128911
negative_passages.text: Continuous extension of a real function
negative_passages.docid: 56429
negative_passages.text: Extension of partial derivatives and the definition of $C^k(\overline{\Omega})$