Ivan Shishkin, Rye (1878)

Problems/Normed vector spaceUnreviewed

Super-échappatoire à l’infini

by La chouette aveugle·
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 EE un espace de Banach de dimension infinie et KK un compact de EE. Soit F=VectR(K)F = \mathrm{Vect}_{\mathbb{R}}(K). Montrer que E∖FE\setminus F est connexe par arcs. Donner un contre-exemple à cette affirmation si EE n’est pas supposé complet.

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