Theorems · Theorem · general topology

CompactSpace.nonempty_sInter

∀ {X : Type u} [inst : TopologicalSpace X] [CompactSpace X] {s : Set (Set X)},
  (∀ t ∈ s, IsClosed t) → (∀ t ⊆ s, t.Finite → (⋂₀ t).Nonempty) → (⋂₀ s).Nonempty

Defined in

Mathlib.Topology.Compactness.Compact

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceCompactSpace