Theorems · Theorem · general topology
TopologicalSpace.isOpen_generateFrom_of_mem
∀ {α : Type u} {g : Set (Set α)} {s : Set α}, s ∈ g → IsOpen s- Defined in
- Mathlib.Topology.Order
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- IsOpenstatement · cited by 2,400
- TopologicalSpace.generateFromstatement · cited by 62
Cited by11
Results whose statement or proof uses this declaration.
- IsOpen.powerset_vietorisproof · cited by 11
- ContinuousMap.isOpen_setOfPred_mapsToproof · cited by 9
- TopologicalSpace.vietoris.isOpen_inter_nonempty_of_isOpenproof · cited by 8
- CompleteType.isOpen_typesWithproof · cited by 2
- generateFrom_insert_of_generateOpenproof · cited by 2
- TopologicalSpace.eq_induced_by_maps_to_sierpinskiproof · cited by 1
- TopologicalSpace.exists_countable_of_generateFromproof · cited by 1
- regularSpace_generateFromproof · cited by 0
- isTopologicalBasis_biInter_Ioi_Iio_of_generateFromproof · cited by 0
- IsCompact.isOpen_constructibleTopology_of_isClosedproof · cited by 0
- IsCompact.isOpen_constructibleTopology_of_isOpenproof · cited by 0