Theorems · Theorem · general topology

isTotallyDisconnected_of_image

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] {s : Set α} [inst_1 : TopologicalSpace β] {f : α → β},
  ContinuousOn f s → Function.Injective f → IsTotallyDisconnected (f '' s) → IsTotallyDisconnected s

Defined in

Mathlib.Topology.Connected.TotallyDisconnected

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace