Theorems · Theorem · general topology

Topology.IsCoinducing.of_isOpen_preimage_iff_isOpen

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

Alias of the reverse direction of Topology.isCoinducing_iff.

Defined in

Mathlib.Topology.Maps.Basic

Cited by

6 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace