Theorems · Theorem · general topology

TopologicalSpace.IsOpenCover.isOpen_iff_coe_preimage

∀ {β : Type u_2} [inst : TopologicalSpace β] {ι : Type u_3} {U : ι → TopologicalSpace.Opens β} {s : Set β},
  TopologicalSpace.IsOpenCover U → (IsOpen s ↔ ∀ (i : ι), IsOpen (Subtype.val ⁻¹' s))

Defined in

Mathlib.Topology.LocalAtTarget

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace