query: On the existence of homotopy between continuous and differentiable
positive_passages.docid: 143467
positive_passages.text: Continuous maps between compact manifolds are homotopic to smooth ones
negative_passages.docid: 156904
negative_passages.text: Homotopy Extension Property: necessary and sufficient condition
negative_passages.docid: 28315
negative_passages.text: Monotone functions and non-vanishing of derivative
negative_passages.docid: 42900
negative_passages.text: Locally continuously differentiable implies locally Lipschitz
negative_passages.docid: 86993
negative_passages.text: Differentiable injective function betweem manifolds
negative_passages.docid: 147758
negative_passages.text: Differentiable but not continuously differentiable.
negative_passages.docid: 130748
negative_passages.text: Infinitely differentiable function with given zero set?
negative_passages.docid: 93986
negative_passages.text: Connectivity, Path Connectivity and Differentiability
negative_passages.docid: 129716
negative_passages.text: Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that
negative_passages.docid: 111458
negative_passages.text: Prove that $f$ is differentiable
negative_passages.docid: 150447
negative_passages.text: Prove a differentiable function between banach spaces is continuous
negative_passages.docid: 37850
negative_passages.text: Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
negative_passages.docid: 35671
negative_passages.text: Why can a discontinuous function not be differentiable?
negative_passages.docid: 95187
negative_passages.text: The set of homotopy classes
negative_passages.docid: 44069
negative_passages.text: Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
negative_passages.docid: 145173
negative_passages.text: $f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
negative_passages.docid: 157378
negative_passages.text: On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions