Theorems · Theorem · general topology
IsOpenMap.mapsTo_interior
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsOpenMap f → ∀ {s : Set X} {t : Set Y}, Set.MapsTo f s t → Set.MapsTo f (interior s) (interior t)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 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.MapsTostatement and proof · cited by 732
- interiorstatement and proof · cited by 714
- Set.Subset.rflproof · cited by 255
- IsOpenMapstatement and proof · cited by 253
- interior_subsetproof · cited by 171
- isOpen_interiorproof · cited by 130
- Set.MapsTo.image_subsetproof · cited by 49
- interior_maximalproof · cited by 29
- Set.mapsTo_iff_image_subsetproof · cited by 18
- Set.MapsTo.monoproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- IsOpenMap.image_interior_subsetproof · cited by 6
- IsOpenMap.interior_preimage_subset_preimage_interiorproof · cited by 2
- Balanced.zero_insert_interiorproof · cited by 1