Theorems · Theorem · general topology
IsCompactOpenCovered.id_iff_isOpen_and_isCompact
∀ {S : Type u_1} {U : Set S} [inst : TopologicalSpace S], IsCompactOpenCovered (fun x => id) U ↔ IsOpen U ∧ IsCompact U- Defined in
- Mathlib.Topology.Sets.CompactOpenCovered
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.imageproof · cited by 5,609
- IsOpenstatement and proof · cited by 2,400
- TopologicalSpace.Opensproof · cited by 2,040
- IsCompactstatement and proof · cited by 1,282
- Set.image_congrproof · cited by 533
- TopologicalSpace.Opens.carrierproof · cited by 167
- TopologicalSpace.Opens.is_open'proof · cited by 139
- Set.image_id'proof · cited by 86
- IsCompactOpenCoveredstatement · cited by 18
- IsCompactOpenCovered.iff_of_uniqueproof · cited by 5
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