IsCompact.compl_mem_sets_of_nhdsWithin

∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X},
  IsCompact s → ∀ {f : Filter X}, (∀ x ∈ s, ∃ t ∈ nhdsWithin x s, tᶜ ∈ f) → sᶜ ∈ f

The complement to a compact set belongs to a filter f if each x ∈ s has a neighborhood t within s such that tᶜ belongs to f.

Defined in: Mathlib.Topology.Compactness.Compact
Cited by: 2 results in Mathlib
Foundations: Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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