theorem PiBase.Homeomorph.locallyConnectedSpace {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [TopologicalSpace Y] [h : LocallyConnectedSpace X] (f : X ≃ₜ Y) : LocallyConnectedSpace Y

theorem PiBase.WellDefined.locallyConnectedSpace : WellDefined LocallyConnectedSpace