Theorems · Theorem · general topology

Homeomorph.locallyConnectedSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [i : LocallyConnectedSpace Y]
  (h : X ≃ₜ Y), LocallyConnectedSpace X

If the codomain of a homeomorphism is a locally connected space, then the domain is also a locally connected space.

Defined in

Mathlib.Topology.Homeomorph.Lemmas

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceLocallyConnectedSpace