Theorems · Theorem · general topology

Topology.IsInducing.image_vietoris

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
  Topology.IsInducing f → Topology.IsInducing fun x => f '' x

When Set is equipped with the Vietoris topology, taking the image under an inducing map is inducing.

Defined in

Mathlib.Topology.Sets.VietorisTopology

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace