Why is the triangle inequality property of a metric space important?
94672
Why is the triangle inequality property important for metric spaces?
35573
A closed ball in a metric space is a closed set
36566
Equivalence classes and metric spaces
157753
Show that any set in a metric space can be written as the intersection of open sets
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Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
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whether they are complete metric space
74607
Variation of the metric with respect to the metric
16060
Showing this metric space is complete
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Distances between closed sets on metric spaces
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Prove the empty set is closed for a metric space (X,d).
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Closure of a subset in a metric space
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General Proof for the triangle inequality
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If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
36758
Triangle inequality for L2 norm
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$\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
80274
What is the "topology induced by a metric"?