Theorems · Theorem · general topology
IsOpenMap.coborder_preimage_subset
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
IsOpenMap 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 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Compl.complproof · cited by 2,925
- closureproof · cited by 1,254
- IsOpenMapstatement and proof · cited by 253
- Set.compl_subset_complproof · cited by 50
- Set.preimage_complproof · cited by 43
- coborderstatement and proof · cited by 22
- Set.sdiff_subset_sdiff_leftproof · cited by 20
- IsOpenMap.preimage_closure_subset_closure_preimageproof · cited by 5
- Set.preimage_sdiffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- coborder_preimageproof · cited by 1