Theorems · Theorem · general topology

IsDenseInducing.extend_unique_at

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {i : α → β}
  [inst_2 : TopologicalSpace γ] [T2Space γ] {b : β} {f : α → γ} {g : β → γ} (di : IsDenseInducing i),
  (∀ᶠ (x : α) in Filter.comap i (nhds b), g (i x) = f x) → ContinuousAt g b → di.extend f b = g b

Defined in

Mathlib.Topology.DenseEmbedding

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceT2Space