Theorems · Theorem · category theory

Stonean.extremallyDisconnected_preimage

∀ {X Y Z : Stonean} {f : X ⟶ Z} (i : Y ⟶ Z),
  Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom f) →
    ExtremallyDisconnected
      ↑(⇑(CategoryTheory.ConcreteCategory.hom i) ⁻¹' Set.range ⇑(CategoryTheory.ConcreteCategory.hom f))

Defined in: Mathlib.Topology.Category.Stonean.Limits
Cited by: 1 results in Mathlib
Foundations: Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites35

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
Quiver.Homstatement and proof · cited by 32,603
Set.Elemstatement and proof · cited by 7,166
Set.imageproof · cited by 5,609
Set.preimagestatement and proof · cited by 4,946
Set.rangestatement and proof · cited by 4,705
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
ContinuousMapstatement · cited by 2,491
IsOpenproof · cited by 2,400
TopCatstatement and proof · cited by 1,889

Cited by1

Results whose statement or proof uses this declaration.

Stonean.extremallyDisconnected_pullbackproof · cited by 0