Theorems · Theorem · field theory
NormedField.completeSpace_iff_isComplete_closedBall
∀ {K : Type u_4} [inst : NormedField K], CompleteSpace K ↔ IsComplete (Metric.closedBall 0 1)- Defined in
- Mathlib.Analysis.Normed.Field.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedField
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Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Realstatement and proof · cited by 25,697
- NontriviallyNormedFieldproof · cited by 8,742
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- Norm.normproof · cited by 5,413
- Set.rangeproof · cited by 4,705
- Filter.Tendstoproof · cited by 3,814
- LE.le.transproof · cited by 3,151
- CompleteSpacestatement and proof · cited by 2,532
- Filter.atTopproof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- NormedFieldstatement and proof · cited by 1,084
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