When does the quotient metric reduce to the infimum of the distances of only two points?
49503
Why does the natural quotient metric works in this case?
11455
Connected metric spaces with at least 2 points are uncountable.
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
146967
Understanding equivalent metric spaces
15365
Proving that the triangle inequality holds for a metric on $\mathbb{C}$
14799
How to show that the spherical metric satisfies the triangle inequality?
78108
Do these define metrics on $\mathbb{R}$?
84791
Is every connected metric space with at least two points uncountable?
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?
147287
Is it possible to construct a metric in $\mathbb{R}^n $ s.t. it does not induce CONVEX balls?
28006
The minimum of two independent geometric random variables
114047
Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$
45581
Is the distance function in a metric space (uniformly) continuous?
94672
Why is the triangle inequality property important for metric spaces?
20164
Is there always an equivalent metric which is not complete?
142652
When is the product of two quotient maps a quotient map?
114786
Question about Infimum. (conclusion about intersection)