Ivan Shishkin, Rye (1878)

Problems/Set theoryExerciseUnreviewed

Unicité essentielle de la limite inductive

by La chouette aveugle·
40
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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
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These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Soit ((Eα)α,(fβ,α)α≤β)((E_{\alpha})_{\alpha},(f_{\beta,\alpha})_{\alpha \leq \beta}) un système inductif d’ensembles. On suppose que ce système admet une limite inductive(L,(ϕα)α)(\mathcal{L},(\phi_{\alpha})_{\alpha}). Soit (L,(ψα)α)(\mathcal{L},(\psi_{\alpha})_{\alpha}) une autre limite inductive du même système. Montrer que L\mathcal{L} et L′\mathcal{L}' sont en bijection.

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