Theorems · Theorem · general topology
IsOpenMap.image_mem_nhds
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
IsOpenMap f → ∀ {x : X} {s : Set X}, s ∈ nhds x → f '' s ∈ nhds (f x)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 60 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
- Filterstatement · cited by 8,121
- Set.imagestatement and proof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- IsOpenproof · cited by 2,400
- IsOpen.mem_nhdsproof · cited by 470
- Set.mem_image_of_memproof · cited by 371
- Filter.mem_of_supersetproof · cited by 308
- IsOpenMapstatement and proof · cited by 253
- Set.image_monoproof · cited by 197
- mem_nhds_iffproof · cited by 67
Cited by10
Results whose statement or proof uses this declaration.
- IsOpenMap.nhds_leproof · cited by 11
- isOpenMap_smul_of_sigmaCompactproof · cited by 1
- Convex.span_tangentConeAtproof · cited by 1
- isOpenMap_vadd_of_sigmaCompactproof · cited by 1
- closure_subset_add_left_of_mem_nhds_zero_of_negproof · cited by 1
- closure_subset_add_right_of_mem_nhds_zero_of_negproof · cited by 1
- closure_subset_mul_left_of_mem_nhds_one_of_invproof · cited by 1
- closure_subset_mul_right_of_mem_nhds_one_of_invproof · cited by 1
- IsOpenQuotientMap.weaklyLocallyCompactSpaceproof · cited by 0
- IsOpenQuotientMap.locallyCompactSpaceproof · cited by 0