Theorems · Theorem · general topology

IsPreirreducible.preimage_of_isPreirreducible_fiber

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {V : Set Y},
  IsPreirreducible V →
    ∀ (f : X → Y), IsOpenMap f → (∀ (x : Y), IsPreirreducible (f ⁻¹' {x})) → IsPreirreducible (f ⁻¹' V)

Defined in: Mathlib.Topology.Irreducible
Cited by: 3 results in Mathlib
Foundations: Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace 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.ofPredproof · cited by 6,101
Set.preimagestatement and proof · cited by 4,946
closureproof · cited by 1,254
IsOpenMapstatement and proof · cited by 253
Set.inter_univproof · cited by 198
IsPreirreduciblestatement and proof · cited by 43
IsPreirreducible.preimage_of_dense_isPreirreducible_fiberproof · cited by 1

Cited by3

Results whose statement or proof uses this declaration.

IsIrreducible.preimage_of_isPreirreducible_fiberproof · cited by 3
IsPreirreducible.preimageproof · cited by 2
image_mem_irreducibleComponents_of_isPreirreducible_fiberproof · cited by 0