Ivan Shishkin, Rye (1878)

Problems/TopologyExerciseReviewed

The discrete metric

by Ancient Tree·
23
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
English
EnglishFrançais

Let XX be a non-empty set. Show that the function d ⁣:X×X→Rd\colon X\times X\to \R such that:
∀x,y∈X,d(x,y)={1 if x≠y0 otherwise \forall x,y\in X, d(x, y)= \begin{cases}1 & \text { if } x\neq y \\ 0 & \text { otherwise }\end{cases}is a metric on any set XX. It is called the discrete metric.

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