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Theorems · Theorem · general topology

PreconnectedSpace.constant

∀ {α : Type u} [inst : TopologicalSpace α] {Y : Type u_3} [inst_1 : TopologicalSpace Y] [DiscreteTopology Y],
  PreconnectedSpace α → ∀ {f : α → Y}, Continuous f → ∀ {x y : α}, f x = f y

A PreconnectedSpace version of isPreconnected.constant

Defined in
Mathlib.Topology.Connected.TotallyDisconnected
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceDiscreteTopology
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsPreconnected.constant_of_mapsTo · cited by 1IsPreconnected.constant_o…TopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousDiscreteTopology · cited by 373DiscreteTopologyContinuous.continuousOn · cited by 311Continuous.continuousOnPreconnectedSpace · cited by 64PreconnectedSpacePreconnectedSpace.isPreconnected_univ · cited by 26PreconnectedSpace.isPreco…IsPreconnected.constant · cited by 1IsPreconnected.constantPreconnectedSpace.constantCITED BYCITES

Cites7

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Cited by1

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