Theorems · Theorem · general topology

isOpenMap_iff_closure_kernImage

∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
  IsOpenMap f ↔ ∀ {s : Set X}, closure (Set.kernImage f s) ⊆ Set.kernImage f (closure s)

A map is open if and only if the Set.kernImage of every closed set is closed.

Defined in

Mathlib.Topology.Maps.Basic

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace