query: Is the mapping $ q \mapsto \|f\|_{L^q(U)}$ continuous?
positive_passages.docid: 121957
positive_passages.text: Is $p\mapsto \|f\|_p$ continuous?
negative_passages.docid: 149095
negative_passages.text: $f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
negative_passages.docid: 53841
negative_passages.text: Function always continuous in a Sobolev Space?
negative_passages.docid: 33129
negative_passages.text: A linear map $S:Y^*\to X^*$ is weak$^*$ continuous if and only if $S=T^*$ for som $T\in B(X,Y)$
negative_passages.docid: 106256
negative_passages.text: Continuous mapping on a compact metric space is uniformly continuous
negative_passages.docid: 129551
negative_passages.text: Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
negative_passages.docid: 34940
negative_passages.text: Continuity of $f(x) = x^n$
negative_passages.docid: 83676
negative_passages.text: Condition for continuity of bilinear form
negative_passages.docid: 56567
negative_passages.text: Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
negative_passages.docid: 52922
negative_passages.text: let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
negative_passages.docid: 40209
negative_passages.text: $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
negative_passages.docid: 47381
negative_passages.text: If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
negative_passages.docid: 17223
negative_passages.text: Continuity of an inverse function.
negative_passages.docid: 121264
negative_passages.text: Prove that rank $(g \circ f)\le \min[\operatorname{rank}(f),\operatorname{rank}(g)]$; $g$ and $f$ are linear mappings
negative_passages.docid: 60700
negative_passages.text: Continuity of a function to the integers
negative_passages.docid: 106531
negative_passages.text: A Fourier transform of a continuous $L^1$ function
negative_passages.docid: 83494
negative_passages.text: Uniform continuity of $\ln(x)$