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Theorems · Theorem · general topology

IsLocallyConstant.eq_const

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [PreconnectedSpace X] {f : X → Y},
  IsLocallyConstant f → ∀ (x : X), f = Function.const X (f x)
Defined in
Mathlib.Topology.LocallyConstant.Basic
Cited by
2 results in Mathlib
Foundations
Depth 60 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.exists_eq_const · cited by 1IsLocallyConstant.exists_…ProbabilityTheory.gaussian_charFunDual_congr · cited by 1ProbabilityTheory.gaussia…TopologicalSpace · cited by 24529TopologicalSpacePreconnectedSpace · cited by 64PreconnectedSpaceIsLocallyConstant · cited by 51IsLocallyConstantIsLocallyConstant.apply_eq_of_preconnectedSpace · cited by 2IsLocallyConstant.apply_e…IsLocallyConstant.eq_constCITED BYCITES

Cites4

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Cited by2

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