Theorems · Theorem · general topology
Topology.IsGeneratedBy.le_generatedBy
∀ {ι : Type t} {X : ι → Type u} [inst : (i : ι) → TopologicalSpace (X i)] {Y : Type v} {tY : TopologicalSpace Y}
[Topology.IsGeneratedBy X Y], tY ≤ TopologicalSpace.generatedBy X- Defined in
- Mathlib.Topology.Convenient.GeneratedBy
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenproof · cited by 2,400
- Continuous.isOpen_preimageproof · cited by 51
- Topology.IsGeneratedBystatement and proof · cited by 38
- TopologicalSpace.generatedBystatement · cited by 12
- Topology.IsGeneratedBy.continuous_equiv_symmproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Topology.IsGeneratedBy.iSupproof · cited by 2
- Topology.IsGeneratedBy.iff_le_generatedByproof · cited by 2
- Topology.IsGeneratedBy.generatedBy_eqproof · cited by 2