EDB — 0R3

Exercises

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

   \begin{equation} 𝛿(x,y) = \inf \{ d(s,t) : s∈ x, t∈ y \} ~ ~ .\label{eq:dist_ quoziente} \end{equation}

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

   Solution 1

   [0R4]↺↻