query: $C^{1}[0,1]$ is not Banach under $\|\cdot\|_{\infty}$
positive_passages.docid: 43826
positive_passages.text: Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
negative_passages.docid: 129087
negative_passages.text: Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
negative_passages.docid: 101701
negative_passages.text: Prove that $\ln x$ is not uniformly continuous on $(0,1]$
negative_passages.docid: 146839
negative_passages.text: Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
negative_passages.docid: 118272
negative_passages.text: Show that $L^1$ is strictly contained in $(L^\infty)^*$
negative_passages.docid: 98282
negative_passages.text: Prove that the function $\xi\in R \mapsto {e^{i\cdot \xi\cdot λ}-1\over i\cdot \xi}-λ$ is $C^{\infty}$
negative_passages.docid: 58456
negative_passages.text: Why is $ 1^{\infty} \not= \lim_{t \to \infty} 1^t = 1$?
negative_passages.docid: 157203
negative_passages.text: Let $\{f_k\}_{k=1}^\infty\in L^{loc}_1(\mathbb R^n)$, show $\{f_k^2\}_{k=1}^\infty$ does not converge in $\mathscr{D}^\prime(\mathbb R^n)$
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 12467
negative_passages.text: Why does this proof work: Closed unit ball in $C_0$ is not compact
negative_passages.docid: 36227
negative_passages.text: Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
negative_passages.docid: 14840
negative_passages.text: $c_0$ is a closed subspace of $l^{\infty}$
negative_passages.docid: 42108
negative_passages.text: Prove that $c_0$ is closed in $\ell^\infty$
negative_passages.docid: 98756
negative_passages.text: Unit ball in $C[0,1]$ not sequentially compact
negative_passages.docid: 139272
negative_passages.text: On the norm of a quotient of a Banach space.
negative_passages.docid: 157455
negative_passages.text: Show that the norm of the multiplication operator $M_f$ on $L^2[0,1]$ is $\|f\|_\infty$
negative_passages.docid: 63285
negative_passages.text: Prove that this space is not Banach