query: Why do we care if a function is uniformly continuous?
positive_passages.docid: 147152
positive_passages.text: Why did mathematicians introduce the concept of uniform continuity?
negative_passages.docid: 102315
negative_passages.text: difference of uniform continuity and continuity of map
negative_passages.docid: 10898
negative_passages.text: Is an integral always continuous?
negative_passages.docid: 98772
negative_passages.text: Continuity of a function in $\mathbb{R}$
negative_passages.docid: 113086
negative_passages.text: Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
negative_passages.docid: 129073
negative_passages.text: If $f'$ is bounded, then $f$ is uniformly continuous
negative_passages.docid: 141945
negative_passages.text: Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
negative_passages.docid: 86327
negative_passages.text: If the absolute value of a function is continuous, is the function continuous?
negative_passages.docid: 136011
negative_passages.text: Must $f$ be continuous?
negative_passages.docid: 73585
negative_passages.text: Why is the function continuous, if it is defined only on integers?
negative_passages.docid: 33488
negative_passages.text: A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
negative_passages.docid: 47188
negative_passages.text: Uniformly Continuous Function sending Bounded Set to Unbounded One
negative_passages.docid: 28730
negative_passages.text: product of two uniformly continuous functions is uniformly continuous
negative_passages.docid: 53841
negative_passages.text: Function always continuous in a Sobolev Space?
negative_passages.docid: 45395
negative_passages.text: Difference between continuity and uniform continuity
negative_passages.docid: 83494
negative_passages.text: Uniform continuity of $\ln(x)$
negative_passages.docid: 93461
negative_passages.text: Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.