Theorems · Theorem · general topology

Continuous.image_connectedComponent_subset

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
  Continuous f → ∀ (a : α), f '' connectedComponent a ⊆ connectedComponent (f a)

Defined in

Mathlib.Topology.Connected.Basic

Cited by

6 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace