query: Let (X, d) be a metric space. Show that the metric d is continuous.
positive_passages.docid: 23845
positive_passages.text: How to prove the continuity of the metric function?
negative_passages.docid: 7402
negative_passages.text: Showing a compact metric space has a countable dense subset
negative_passages.docid: 55605
negative_passages.text: If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
negative_passages.docid: 130299
negative_passages.text: Prove that if a function $f: X\to Y$ continuous then its graph is closed
negative_passages.docid: 17067
negative_passages.text: To prove that $(\mathbb{P(N)},d)$ is a metric space
negative_passages.docid: 126944
negative_passages.text: Metric spaces problem
negative_passages.docid: 112329
negative_passages.text: Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
negative_passages.docid: 26547
negative_passages.text: Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
negative_passages.docid: 140052
negative_passages.text: Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
negative_passages.docid: 15480
negative_passages.text: Open set in a metric space is union of closed sets
negative_passages.docid: 13848
negative_passages.text: Showing that if a subset of a complete metric space is closed, it is also complete
negative_passages.docid: 32359
negative_passages.text: Inner product of two continuous maps is continuous
negative_passages.docid: 60521
negative_passages.text: Continuity of a convex function
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: 100740
negative_passages.text: proof of that a continuous function has a fixed point
negative_passages.docid: 152493
negative_passages.text: Is an expanding map on a compact metric space continuous?
negative_passages.docid: 123061
negative_passages.text: $X$ metric separable then $C(X)$ separable