Theorems · Theorem · general topology

TopologicalSpace.NoetherianSpace.exists_finite_set_closeds_irreducible

∀ {α : Type u_1} [inst : TopologicalSpace α] [TopologicalSpace.NoetherianSpace α] (s : TopologicalSpace.Closeds α),
  ∃ S, S.Finite ∧ (∀ t ∈ S, IsIrreducible ↑t) ∧ s = sSup S

In a Noetherian space, every closed set is a finite union of irreducible closed sets.

Defined in

Mathlib.Topology.NoetherianSpace

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace.NoetherianSpace