Theorems · Theorem · general topology
Inseparable.mem_open_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] {x y : X} {s : Set X}, Inseparable x y → IsOpen s → (x ∈ s ↔ y ∈ s)- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsOpenstatement and proof · cited by 2,400
- Inseparablestatement and proof · cited by 160
- inseparable_iff_forall_isOpenproof · cited by 3
Cited by11
Results whose statement or proof uses this declaration.
- IsCompact.closure_subset_of_isOpenproof · cited by 9
- TendstoLocallyUniformlyOn.congr_inseparable_rightproof · cited by 4
- TendstoUniformlyOn.congr_inseparable_rightproof · cited by 3
- TendstoUniformlyOnFilter.congr_inseparableproof · cited by 2
- SeparationQuotient.preimage_image_mk_openproof · cited by 2
- TendstoLocallyUniformlyOn.congr_inseparableproof · cited by 2
- exists_mem_nhds_isCompact_mapsTo_of_isCompact_mem_nhdsproof · cited by 1
- SeparationQuotient.comap_map_mk_uniformityproof · cited by 1
- Inseparable.mem_measurableSet_iffproof · cited by 1
- IsOpen.not_inseparableproof · cited by 0
- T0Space.of_open_coverproof · cited by 0