Theorems · Theorem · general topology

Topology.IsInducing.map_nhdsSet_eq

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
  Topology.IsInducing f → ∀ (s : Set α), Filter.map f (nhdsSet s) = nhdsSetWithin (f '' s) (Set.range f)

Defined in

Mathlib.Topology.NhdsWithin

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace