EDB — 0R3

Exercises

1. [0R3] Let $(X,d)$ be a metric space and $\sim$ an equivalence relation on $X$. Let $Y=X/\sim$ be the quotient space. We define the function $𝛿:Y^2\to ℝ$ as

   $$\begin{array}{}\text{(1)}& 𝛿(x,y)=inf\{d(s,t):s\in x,t\in y\}.\end{array}$$

   57

   Is it a distance on $Y$? Which properties does it enjoy among those indicated in [0MS]↺↻?

   Solution 1

   [0R4]↺↻