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Showing equivalent metrics have the same convergent sequences
general-topology
metric-spaces
equivalent-metrics
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
metric-spaces
equivalent-metrics
Prove $\frac{1}{\sqrt{n}}\|A\|_{\infty} \leq\|A\|_{2} \leq \sqrt{m}\|A\|_{\infty} $
linear-algebra
inequality
normed-spaces
matrix-norms
equivalent-metrics
Equivalent metrics using open balls
general-topology
metric-spaces
equivalent-metrics
Understanding the concepts of topologies and equivalent metrics
real-analysis
general-topology
metric-spaces
compactness
equivalent-metrics
About $\rho(x, y)= \begin{cases}\mathrm{d}(x, y) & \mathrm{d}(x, y)<1 \\ 1 & \mathrm{~d}(x, y) \geq 1\end{cases}$ in a metric space
real-analysis
general-topology
metric-spaces
examples-counterexamples
equivalent-metrics
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