Theorems · Theorem · general topology

IsCompactOpenCovered.of_finite_of_isSpectralMap

∀ {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)]
  [Finite ι] [inst_2 : TopologicalSpace S],
  (∀ (i : ι), IsSpectralMap (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: 0 results in Mathlib
Foundations: Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace Finite TopologicalSpace

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Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Set.imageproof · cited by 5,609
Set.preimageproof · cited by 4,946
Set.rangestatement and proof · cited by 4,705
Set.univproof · cited by 3,945
Finitestatement and proof · cited by 3,029
Set.iUnionproof · cited by 2,483
IsOpenstatement and proof · cited by 2,400
IsCompactstatement and proof · cited by 1,282
Set.iUnion_congr_Propproof · cited by 374
subset_antisymmproof · cited by 150

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