Theorems · Definition · general topology

TopologicalSpace.IrreducibleCloseds.orderIsoOfIsOpenEmbedding

{α : Type u_2} →
  {β : Type u_3} →
    [inst : TopologicalSpace α] →
      [inst_1 : TopologicalSpace β] →
        (f : β → α) → Topology.IsOpenEmbedding f → TopologicalSpace.IrreducibleCloseds β ≃o ↑{V | (f ⁻¹' ↑V).Nonempty}

Given f : U → X a continuous open embedding, the irreducible closeds of U are order isomorphic to the irreducible closeds of X nontrivially intersecting the range of f.

Defined in

Mathlib.Topology.Sets.Closeds

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace