Metric function proof
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
3537
Show the Euclidean metric and maximum metric are strongly equivalent.
138607
Proof that a limit point compact metric space is compact.
71619
Proving that a convex function is Lipschitz
27652
metric on the Euclidean Group
39763
Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure
125682
Proof verification: the product of two continuous functions is continuous
140124
The distance function on a metric space
95831
Compactness and sequential compactness in metric spaces
94672
Why is the triangle inequality property important for metric spaces?
7402
Showing a compact metric space has a countable dense subset
50677
Is this metric space incomplete?
65809
Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric
35291
How to show $d(x,y)= \sqrt{d_1(x_1,y_1)^2+d_2(x_2,y_2)^2}$ is a metric?
13848
Showing that if a subset of a complete metric space is closed, it is also complete
123753
In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$