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Theorems · Theorem · general topology

GeneralizingMap_iff_stableUnderGeneralization_image

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  GeneralizingMap f ↔ ∀ (s : Set X), StableUnderGeneralization s → StableUnderGeneralization (f '' s)
Defined in
Mathlib.Topology.Inseparable
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Foundations
Depth 21 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.image · cited by 5609Set.imageStableUnderGeneralization · cited by 24StableUnderGeneralizationGeneralizingMap · cited by 16GeneralizingMapRelation.fibration_iff_isUpperSet_image · cited by 1Relation.fibration_iff_is…GeneralizingMap_iff_stableUnd…CITED BYCITES

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