Theorems · Theorem · general topology

Homeomorph.image_connectedComponentIn

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} (h : X ≃ₜ Y)
  {x : X}, x ∈ s → ⇑h '' connectedComponentIn s x = connectedComponentIn (⇑h '' s) (h x)

Defined in

Mathlib.Topology.Homeomorph.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace