Theorems · Theorem · general topology
le_generateFrom
∀ {α : Type u} {t : TopologicalSpace α} {g : Set (Set α)}, (∀ s ∈ g, IsOpen s) → t ≤ TopologicalSpace.generateFrom g- Defined in
- Mathlib.Topology.Order
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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
- TopologicalSpace.generateFromstatement · cited by 62
- TopologicalSpace.le_generateFrom_iff_subset_isOpenproof · cited by 5
Cited by10
Results whose statement or proof uses this declaration.
- TopologicalSpace.isTopologicalBasis_of_subbasisproof · cited by 6
- induced_generateFrom_eqproof · cited by 5
- pi_generateFrom_eqproof · cited by 2
- generateFrom_insert_of_generateOpenproof · cited by 2
- ContinuousMap.compactOpen_eq_iInf_inducedproof · cited by 2
- Dense.topology_eq_generateFromproof · cited by 1
- prod_generateFrom_generateFrom_eqproof · cited by 0
- le_induced_generateFromproof · cited by 0
- pi_generateFrom_eq_finiteproof · cited by 0
- prod_eq_generateFromproof · cited by 0