query: bounded monotone continuous function is uniform continuous
positive_passages.docid: 143695
positive_passages.text: Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
negative_passages.docid: 47188
negative_passages.text: Uniformly Continuous Function sending Bounded Set to Unbounded One
negative_passages.docid: 14067
negative_passages.text: If f uniformly continous then $|f(x)|\leq C\cdot (1+|x|)$ for constant C
negative_passages.docid: 123972
negative_passages.text: Proving that every function defined on a discrete metric space is uniformly continuous.
negative_passages.docid: 110458
negative_passages.text: Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
negative_passages.docid: 50730
negative_passages.text: Integral of bounded continuous function on $R$
negative_passages.docid: 41847
negative_passages.text: Uniformly continuous function with unbounded variation
negative_passages.docid: 123981
negative_passages.text: Is it possible to write any bounded continuous function as a uniform limit of smooth functions
negative_passages.docid: 51247
negative_passages.text: $f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
negative_passages.docid: 127449
negative_passages.text: Uniform continuous of $f(x,y) = \sin(x^2+y)$
negative_passages.docid: 36166
negative_passages.text: Uniform continuity on (0,1) implies boundedness
negative_passages.docid: 66691
negative_passages.text: Real function continuous on closed interval implies it is bounded - over-simple proof??
negative_passages.docid: 158344
negative_passages.text: Uniform continuous maps that converge uniformly to a function f. What can we say about f?
negative_passages.docid: 31741
negative_passages.text: Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
negative_passages.docid: 132869
negative_passages.text: Show that any bounded linear functional on a normed linear space is continuous
negative_passages.docid: 106060
negative_passages.text: If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
negative_passages.docid: 99179
negative_passages.text: Continuous function with compact domain has continuous inverse