Theorems · Theorem · general topology
Topology.IsOpenEmbedding.coborder_preimage
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsOpenEmbedding f → ∀ (s : Set Y), coborder (f ⁻¹' s) = f ⁻¹' coborder s- Defined in
- Mathlib.Topology.LocallyClosed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 4,946
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsOpenEmbedding.isOpenMapproof · cited by 50
- Topology.IsOpenEmbedding.continuousproof · cited by 23
- coborderstatement · cited by 22
- coborder_preimageproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.IsOpenCover.isLocallyClosed_iff_coe_preimageproof · cited by 0