Theorems · Theorem · general topology
IsClosedMap.closure_image_subset
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsClosedMap f → ∀ (s : Set X), closure (f '' s) ⊆ f '' closure s- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 7 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.
Cites9
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
- closurestatement and proof · cited by 1,254
- subset_closureproof · cited by 309
- Set.image_monoproof · cited by 197
- isClosed_closureproof · cited by 195
- IsClosedMapstatement and proof · cited by 138
- closure_minimalproof · cited by 94
Cited by7
Results whose statement or proof uses this declaration.
- IsClosedMap.closure_image_eq_of_continuousproof · cited by 6
- isClosedMap_iff_closure_imageproof · cited by 1
- NonUnitalSubalgebra.topologicalClosure_map_leproof · cited by 0
- Subalgebra.topologicalClosure_map_leproof · cited by 0
- NonUnitalStarSubalgebra.topologicalClosure_map_leproof · cited by 0
- SeparationQuotient.image_mk_closureproof · cited by 0
- StarSubalgebra.topologicalClosure_map_leproof · cited by 0