Theorems · Theorem · general topology

Topology.IsCoinducing.connectedComponentsHomeomorph_symm_mk_apply

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
  (hf : Topology.IsCoinducing f) (hf' : ∀ (y : Y), IsConnected (f ⁻¹' {y})) (x : X),
  (hf.connectedComponentsHomeomorph hf').symm (ConnectedComponents.mk (f x)) = ConnectedComponents.mk x

Defined in

Mathlib.Topology.Homeomorph.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace