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Theorems · Theorem · general topology

preconnectedSpace_of_forall_constant

∀ {α : Type u} [inst : TopologicalSpace α],
  (∀ (f : α → Bool), Continuous f → ∀ (x y : α), f x = f y) → PreconnectedSpace α

A PreconnectedSpace version of isPreconnected_of_forall_constant

Defined in
Mathlib.Topology.Connected.Clopen
Cited by
1 results in Mathlib
Foundations
Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

preconnectedSpace_iff_clopen · cited by 3preconnectedSpace_iff_clo…TopologicalSpace · cited by 24529TopologicalSpaceSet.univ · cited by 3945Set.univContinuous · cited by 2592ContinuousContinuousOn · cited by 1411ContinuousOnPreconnectedSpace · cited by 64PreconnectedSpacecontinuousOn_univ · cited by 43continuousOn_univisPreconnected_of_forall_constant · cited by 1isPreconnected_of_forall_…preconnectedSpace_of_forall_c…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.