Theorems · Theorem · general topology

Homeomorph.isPathConnected_preimage

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set Y} (h : X ≃ₜ Y),
  IsPathConnected (⇑h ⁻¹' s) ↔ IsPathConnected s

If h : X → Y is a homeomorphism, h⁻¹(s) is path-connected iff s is.

Defined in

Mathlib.Topology.Connected.PathConnected

Cited by

0 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace