Theorems · Theorem · general topology
SigmaCompactSpace.of_countable
∀ {X : Type u_1} [inst : TopologicalSpace X] (S : Set (Set X)),
S.Countable → (∀ s ∈ S, IsCompact s) → ⋃₀ S = Set.univ → SigmaCompactSpace X- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement and proof · cited by 3,945
- IsCompactstatement and proof · cited by 1,282
- Set.Countablestatement and proof · cited by 545
- Set.sUnionstatement and proof · cited by 392
- SigmaCompactSpacestatement · cited by 55
- isCompact_emptyproof · cited by 17
- Set.exists_seq_cover_iff_countableproof · cited by 2
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