Theorems · Theorem · general topology

isOpenMap_iff_nhds_le

∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
  IsOpenMap f ↔ ∀ (x : X), nhds (f x) ≤ Filter.map f (nhds x)

Defined in

Mathlib.Topology.Maps.Basic

Cited by

6 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace