Theorems · Theorem · general topology

isClosedMap_iff_comap_nhds_le

∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
  IsClosedMap f ↔ ∀ {y : Y}, Filter.comap f (nhds y) ≤ nhdsSet (f ⁻¹' {y})

Defined in

Mathlib.Topology.Maps.Basic

Cited by

3 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace