Theorems · Theorem · general topology

TotallyDisconnectedSpace.eq_of_continuous

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] [PreconnectedSpace α]
  [TotallyDisconnectedSpace β] (f : α → β), Continuous f → ∀ (i j : α), f i = f j

Defined in

Mathlib.Topology.Connected.TotallyDisconnected

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpacePreconnectedSpaceTotallyDisconnectedSpace