query: If f and g are uniformly continuous then fg is uniformly continuous
positive_passages.docid: 28730
positive_passages.text: product of two uniformly continuous functions is uniformly continuous
negative_passages.docid: 138815
negative_passages.text: For which conditions on countable sets does continuity implies uniform continuity
negative_passages.docid: 108057
negative_passages.text: If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
negative_passages.docid: 50366
negative_passages.text: Convolution is uniformly continuous and bounded
negative_passages.docid: 34836
negative_passages.text: Composition of Absolutely Continuous Functions
negative_passages.docid: 129856
negative_passages.text: Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
negative_passages.docid: 46629
negative_passages.text: Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
negative_passages.docid: 89568
negative_passages.text: Uniform continuity on $[a,b]$ and $ [b,c]$ $\implies$ uniform continuity on $[a,c]$.
negative_passages.docid: 34940
negative_passages.text: Continuity of $f(x) = x^n$
negative_passages.docid: 57023
negative_passages.text: If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
negative_passages.docid: 4062
negative_passages.text: prove that $f(x)=\log(1+x^2)$ is Uniform continuous with $\epsilon ,\delta$ ...
negative_passages.docid: 132946
negative_passages.text: Continuous and bounded imply uniform continuity?
negative_passages.docid: 128069
negative_passages.text: Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
negative_passages.docid: 57642
negative_passages.text: Uniform Continuity implies Continuity
negative_passages.docid: 16735
negative_passages.text: If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
negative_passages.docid: 51247
negative_passages.text: $f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
negative_passages.docid: 104044
negative_passages.text: Prove continuous functions $f$ and $g$ are equal