Ivan Shishkin, Rye (1878)

Problems/TopologyExerciseUnreviewed

Les ouverts d’un espace métrique forment une topologie

by SalixBabylonica·
50
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.
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Soit (E,d)(E,d) un espace métrique. On note
T={U⊂E  ;  ∀x∈U, ∃r>0 tel que B(x,r)⊂U}.\mathcal T = \bigl\{ U\subset E \; ; \; \forall x\in U,\ \exists r>0 \text{ tel que } B(x,r)\subset U \bigr\}.Autrement dit, T\mathcal T est l’ensemble des ouverts de (E,d)(E,d).
Montrer que T\mathcal T est une topologie sur EE

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