Theorems · Theorem · general topology

minimal_nonempty_closed_eq_singleton

∀ {X : Type u_1} [inst : TopologicalSpace X] [T0Space X] {s : Set X},
  IsClosed s → s.Nonempty → (∀ t ⊆ s, t.Nonempty → IsClosed t → t = s) → ∃ x, s = {x}

Defined in

Mathlib.Topology.Separation.Basic

Cited by

2 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT0Space