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Theorems · Theorem · general topology

IsLocallyConstant.apply_eq_of_preconnectedSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [PreconnectedSpace X] {f : X → Y},
  IsLocallyConstant f → ∀ (x y : X), f x = f y
Defined in
Mathlib.Topology.LocallyConstant.Basic
Cited by
2 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpacePreconnectedSpace
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Around this declaration

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

IsLocallyConstant.eq_const · cited by 2IsLocallyConstant.eq_constMDifferentiable.apply_eq_of_compactSpace · cited by 0MDifferentiable.apply_eq_…TopologicalSpace · cited by 24529TopologicalSpacePreconnectedSpace · cited by 64PreconnectedSpaceIsLocallyConstant · cited by 51IsLocallyConstantPreconnectedSpace.isPreconnected_univ · cited by 26PreconnectedSpace.isPreco…IsLocallyConstant.apply_eq_of_isPreconnected · cited by 5IsLocallyConstant.apply_e…IsLocallyConstant.apply_eq_of…CITED BYCITES

Cites5

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Cited by2

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