Theorems · Theorem · general topology

IsOpenQuotientMap.dense_preimage_iff

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  IsOpenQuotientMap f → ∀ {s : Set Y}, Dense (f ⁻¹' s) ↔ Dense s

Defined in

Mathlib.Topology.Maps.OpenQuotient

Cited by

3 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace