Theorems · Theorem · general topology

PrimitiveSpectrum.hull_kernel_of_isClosed

∀ {α : Type u_1} [inst : CompleteLattice α] {T : Set α} [inst_1 : TopologicalSpace α] [Topology.IsLower α],
  (∀ p ∈ T, InfPrime p) →
    PrimitiveSpectrum.OrderGenerates T →
      ∀ {C : Set ↑T}, IsClosed C → PrimitiveSpectrum.hull T (PrimitiveSpectrum.kernel C) = C

Defined in

Mathlib.Topology.Order.HullKernel

Cited by

1 results in Mathlib

Foundations

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

Assumes

CompleteLatticeTopologicalSpaceTopology.IsLower