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Theorems · Theorem · general topology

IsLocallyConstant.of_constant

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] (f : X → Y), (∀ (x y : X), f x = f y) → IsLocallyConstant f
Defined in
Mathlib.Topology.LocallyConstant.Basic
Cited by
2 results in Mathlib
Foundations
Depth 68 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.

IsLocallyConstant.const · cited by 2IsLocallyConstant.constIsLocallyConstant.iff_is_const · cited by 0IsLocallyConstant.iff_is_…TopologicalSpace · cited by 24529TopologicalSpaceFilter.Eventually.of_forall · cited by 526Eventually.of_forallIsLocallyConstant · cited by 51IsLocallyConstantIsLocallyConstant.iff_eventually_eq · cited by 3IsLocallyConstant.iff_eve…IsLocallyConstant.of_constantCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.