Theorems · Theorem · general topology

TopologicalSpace.IsOpenCover.isInducing_iff_restrictPreimage

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {ι : Type u_3}
  {U : ι → TopologicalSpace.Opens β},
  TopologicalSpace.IsOpenCover U →
    Continuous f → (Topology.IsInducing f ↔ ∀ (i : ι), Topology.IsInducing ((U i).carrier.restrictPreimage f))

Defined in

Mathlib.Topology.LocalAtTarget

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace