Theorems · Theorem · general topology

Topology.IsOpenEmbedding.map_nhdsWithin_preimage_eq

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
  Topology.IsOpenEmbedding f → ∀ (s : Set β) (x : α), Filter.map f (nhdsWithin x (f ⁻¹' s)) = nhdsWithin (f x) s

Defined in

Mathlib.Topology.ContinuousOn

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace