Theorems · Theorem · general topology
Metric.Sigma.completeSpace
∀ {ι : Type u_1} {E : ι → Type u_2} [inst : (i : ι) → MetricSpace (E i)] [∀ (i : ι), CompleteSpace (E i)],
CompleteSpace ((i : ι) × E i)A disjoint union of complete metric spaces is complete.
- Defined in
- Mathlib.Topology.MetricSpace.Gluing
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpaceCompleteSpace
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Cites20
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- zero_lt_oneproof · cited by 598
- IsCompleteproof · cited by 68
- Metric.dist_mem_uniformityproof · cited by 23
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