Theorems · Theorem · algebraic geometry

Topology.isConstructible_preimage_iff_of_isOpenEmbedding

∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set Y},
  Topology.IsOpenEmbedding f →
    IsRetrocompact (Set.range f) → s ⊆ Set.range f → (Topology.IsConstructible (f ⁻¹' s) ↔ Topology.IsConstructible s)

Defined in: Mathlib.Topology.Constructible
Cited by: 1 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace

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Cites11

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.preimagestatement and proof · cited by 4,946
Set.rangestatement and proof · cited by 4,705
Topology.IsOpenEmbeddingstatement and proof · cited by 231
Topology.IsConstructiblestatement and proof · cited by 45
IsRetrocompactstatement and proof · cited by 43
Set.inter_eq_rightproof · cited by 41
Set.image_preimage_eq_range_interproof · cited by 11
Topology.IsConstructible.preimage_of_isOpenEmbeddingproof · cited by 6
Topology.IsConstructible.image_of_isOpenEmbeddingproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

Topology.IsConstructible.isLocallyConstructibleproof · cited by 7