Theorems · Theorem · general topology
IsCompactOpenCovered.of_isOpenMap
∀ {S : Type u_1} {ι : Type u_2} {X : ι → Type u_3} {f : (i : ι) → X i → S} [inst : (i : ι) → TopologicalSpace (X i)]
[inst_1 : TopologicalSpace S] [∀ (i : ι), PrespectralSpace (X i)],
(∀ (i : ι), Continuous (f i)) →
(∀ (i : ι), IsOpenMap (f i)) →
∀ {U : Set S}, (∀ x ∈ U, ∃ i, x ∈ Set.range (f i)) → IsOpen U → IsCompact U → IsCompactOpenCovered f U- Defined in
- Mathlib.Topology.Sets.CompactOpenCovered
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.rangestatement and proof · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- IsOpenstatement and proof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- IsOpenMapstatement and proof · cited by 253
- PrespectralSpacestatement and proof · cited by 23
- IsCompactOpenCoveredstatement · cited by 18
- continuous_sigma_iffproof · cited by 7
- IsCompactOpenCovered.iff_of_uniqueproof · cited by 5
- isOpenMap_sigmaproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.QuasiCompactCover.of_isOpenMapproof · cited by 1