query: A function f on a metric space is uniformly continuous iff for every pair of subsets A, B with d(A, B)=0 implies that d'(f(A), f(B))=0
positive_passages.docid: 65346
positive_passages.text: Characterisation of uniformly continuous function
negative_passages.docid: 74364
negative_passages.text: Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
negative_passages.docid: 107701
negative_passages.text: Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
negative_passages.docid: 30965
negative_passages.text: $f$ is continuous on $X$ iff $f$ is continuous on every compact subset
negative_passages.docid: 9406
negative_passages.text: Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
negative_passages.docid: 94781
negative_passages.text: Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
negative_passages.docid: 12997
negative_passages.text: Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?
negative_passages.docid: 23845
negative_passages.text: How to prove the continuity of the metric function?
negative_passages.docid: 45581
negative_passages.text: Is the distance function in a metric space (uniformly) continuous?
negative_passages.docid: 22597
negative_passages.text: Composition of measurable function and continuous function
negative_passages.docid: 64619
negative_passages.text: Continuity of a function of product spaces
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: 64260
negative_passages.text: Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
negative_passages.docid: 95327
negative_passages.text: Lipschitz and uniform continuity
negative_passages.docid: 90619
negative_passages.text: For closed subsets $A,B \subseteq X$ with $X = A \cup B$ show that $f \colon X \to Y$ is continuous iff $f|_A$ and $f|_B$ are continuous.
negative_passages.docid: 151832
negative_passages.text: uniformly convergence on compact metric space
negative_passages.docid: 47419
negative_passages.text: Asymptotics of uniformly continuous functions over $\mathbb R$