Theorems · Theorem · general topology

IsCompactOpenCovered.iff_of_unique

∀ {S : Type u_1} {ι : Type u_2} {X : ι → Type u_3} {f : (i : ι) → X i → S} [inst : (i : ι) → TopologicalSpace (X i)]
  {U : Set S} [inst_1 : Unique ι], IsCompactOpenCovered f U ↔ ∃ V, IsCompact V.carrier ∧ f default '' V.carrier = U

Defined in

Mathlib.Topology.Sets.CompactOpenCovered

Cited by

5 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceUnique