Theorems · Theorem · algebraic geometry
IsRetrocompact.preimage_of_isClosedEmbedding
∀ {X : Type u_2} {Y : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set Y},
Topology.IsClosedEmbedding f → IsCompact (Set.range f)ᶜ → IsRetrocompact s → IsRetrocompact (f ⁻¹' s)[Stacks Tag 09YE](https://stacks.math.columbia.edu/tag/09YE) (Extracted from the proof)
- Defined in
- Mathlib.Topology.Constructible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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.imageproof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Compl.complstatement and proof · cited by 2,925
- IsOpenproof · cited by 2,400
- IsCompactstatement and proof · cited by 1,282
- compl_complproof · cited by 229
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- IsClosed.isOpen_complproof · cited by 126
- IsCompact.imageproof · cited by 105
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsConstructible.preimage_of_isClosedEmbeddingproof · cited by 0