query: Show that a the uniform metric over the set of bounded functions is complete
positive_passages.docid: 143674
positive_passages.text: Space of bounded functions is complete
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 36149
negative_passages.text: A uniformly continuous function maps bounded set to bounded sets
negative_passages.docid: 82745
negative_passages.text: Showing Entire Function is Bounded
negative_passages.docid: 109570
negative_passages.text: How to show that the set of points of continuity is a $G_{\delta}$
negative_passages.docid: 157753
negative_passages.text: Show that any set in a metric space can be written as the intersection of open sets
negative_passages.docid: 137881
negative_passages.text: A not complete metric space?
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 25306
negative_passages.text: A countable family of point-wise bounded functions defined on finite measurable set is actually uniformly bounded on a closed subset
negative_passages.docid: 123972
negative_passages.text: Proving that every function defined on a discrete metric space is uniformly continuous.
negative_passages.docid: 42638
negative_passages.text: Showing that a function $f$ has a unique fixed point in a metric space.
negative_passages.docid: 130537
negative_passages.text: Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
negative_passages.docid: 92588
negative_passages.text: Showing that $(C_0([0,\infty)), \|\cdot\|_\infty)$ is complete.
negative_passages.docid: 107701
negative_passages.text: Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
negative_passages.docid: 84264
negative_passages.text: the space of lipschitz function is complete with respect to some norm
negative_passages.docid: 1864
negative_passages.text: Proving $f$ is Lipschitz given $f_{n}\rightarrow f$ and $f_{n}$ is uniformly Lipschitz
negative_passages.docid: 36166
negative_passages.text: Uniform continuity on (0,1) implies boundedness