Theorems · Theorem · algebraic topology

IsCoveringMapOn.of_isCoveringMap_restrictPreimage

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} (s : Set X),
  IsOpen s → IsOpen (f ⁻¹' s) → IsCoveringMap (s.restrictPreimage f) → IsCoveringMapOn f s

Defined in

Mathlib.Topology.Covering.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace