Theorems · Theorem · general topology
IsOpenMap.interior_preimage_subset_preimage_interior
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsOpenMap f → ∀ {s : Set Y}, interior (f ⁻¹' s) ⊆ f ⁻¹' interior s- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- interiorstatement · cited by 714
- IsOpenMapstatement and proof · cited by 253
- Set.mapsTo_preimageproof · cited by 35
- IsOpenMap.mapsTo_interiorproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsOpenMap.preimage_interior_eq_interior_preimageproof · cited by 8
- IsOpenMap.preimage_closure_subset_closure_preimageproof · cited by 5