Theorems · Theorem · general topology

IsOpenMap.exists_opens_image_eq_of_prespectralSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [PrespectralSpace X]
  {f : X → Y},
  Continuous f →
    IsOpenMap f → ∀ {U : Set Y}, U ⊆ Set.range f → IsOpen U → IsCompact U → ∃ V, IsCompact V.carrier ∧ f '' ↑V = U

If X has a basis of compact opens and f : X → S is open, every compact open of S is the image of a compact open of X.

Defined in

Mathlib.Topology.Spectral.Prespectral

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpacePrespectralSpace