Theorems · Theorem · general topology
PiNat.completeSpace
∀ {E : ℕ → Type u_1} [inst : (n : ℕ) → TopologicalSpace (E n)] [inst_1 : ∀ (n : ℕ), DiscreteTopology (E n)],
CompleteSpace ((n : ℕ) → E n)- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CompleteSpacestatement · cited by 2,532
- Filter.univ_mem'proof · cited by 1,672
- le_rflproof · cited by 1,558
- Dist.distproof · cited by 1,539
- Filter.mp_memproof · cited by 1,537
- Set.Iciproof · cited by 1,070
- one_divproof · cited by 624
- DiscreteTopologystatement and proof · cited by 373
- tendsto_const_nhdsproof · cited by 330
- Filter.Tendsto.congr'proof · cited by 154
- inv_powproof · cited by 140
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