Theorems · Theorem · general topology
IsOpenMap.image_interior_subset
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsOpenMap f → ∀ (s : Set X), f '' interior s ⊆ interior (f '' s)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 6 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.
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.imagestatement · cited by 5,609
- interiorstatement · cited by 714
- IsOpenMapstatement and proof · cited by 253
- Set.mapsTo_imageproof · cited by 71
- Set.MapsTo.image_subsetproof · cited by 49
- IsOpenMap.mapsTo_interiorproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- StrictConvex.addproof · cited by 2
- StrictConvex.linear_imageproof · cited by 2
- isOpenMap_iff_image_interiorproof · cited by 1
- Convex.closure_subset_interior_image_homothety_of_one_ltproof · cited by 1
- StrictConvex.affine_imageproof · cited by 0
- ModularGroup.fdo_eq_interior_fdproof · cited by 0