Ivan Shishkin, Rye (1878)

Problems/TopologyReviewed

Exemples simples d’espaces topologiques

by Nolan_2o·
26
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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Déterminer si les espaces (X,τ)(X,\tau) suivants sont des espaces topologiques:

  1. X=RX=\mathbb R muni de τ={R,∅}\tau = \{\mathbb R, \emptyset\}.
  2. X={0,1}X =\{0,1\} muni de τ={∅,{0},{0,1}}\tau = \{\emptyset,\{0\},\{0,1\}\}.
  3. X=RX=\mathbb R muni de τ={R}\tau = \{\mathbb R\}.
  4. X={a,b,c}X=\{a,b,c\} muni de τ={∅,{a},{a,b},X}\tau=\{\emptyset,\{a\},\{a,b\},X\}.
  5. X={0,1,2}X=\{0,1,2\} muni de τ={∅,{0,1},{1,2},X}\tau=\{\emptyset,\{0,1\},\{1,2\},X\}.
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