Theorems · Theorem · general topology

IsCompact.mem_closure_iff_exists_inseparable

∀ {X : Type u_1} [inst : TopologicalSpace X] [R1Space X] {y : X} {K : Set X},
  IsCompact K → (y ∈ closure K ↔ ∃ x ∈ K, Inseparable x y)

In an R₁ space, a point belongs to the closure of a compact set K if and only if it is topologically inseparable from some point of K.

Defined in

Mathlib.Topology.Separation.Basic

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceR1Space