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Theorems · Theorem · general topology

Topology.IsGeneratedBy.iff_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
2 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Topology.IsGeneratedBy.coinduced · cited by 2IsGeneratedBy.coinducedTopology.IsGeneratedBy.iSup · cited by 2IsGeneratedBy.iSupTopologicalSpace · cited by 24529TopologicalSpaceTopology.IsGeneratedBy · cited by 38Topology.IsGeneratedBycontinuous_def · cited by 21continuous_defTopologicalSpace.generatedBy · cited by 12TopologicalSpace.generate…Topology.IsGeneratedBy.le_generatedBy · cited by 3IsGeneratedBy.le_generate…IsGeneratedBy.iff_le_generate…CITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.