Theorems · Theorem · general topology
TopologicalSpace.generateFrom_anti
∀ {α : Type u_1} {g₁ g₂ : Set (Set α)}, g₁ ⊆ g₂ → TopologicalSpace.generateFrom g₂ ≤ TopologicalSpace.generateFrom g₁- Defined in
- Mathlib.Topology.Order
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, 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 · cited by 24,529
- TopologicalSpace.generateFromstatement · cited by 62
- GaloisConnection.monotone_uproof · cited by 53
- TopologicalSpace.gc_generateFromproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- TopologicalSpace.isTopologicalBasis_of_subbasisproof · cited by 6
- generateFrom_insert_of_generateOpenproof · cited by 2
- Dense.topology_eq_generateFromproof · cited by 1
- ContinuousMap.compactOpen_eq_generateFromproof · cited by 1
- exists_countable_generateFrom_Ioi_Iioproof · cited by 0
- pi_generateFrom_eq_finiteproof · cited by 0