Theorems · Theorem · general topology

IsDenseInducing.extend_unique

∀ {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] {f : α → γ} {g : β → γ} (di : IsDenseInducing i),
  (∀ (x : α), g (i x) = f x) → Continuous g → di.extend f = g

Defined in

Mathlib.Topology.DenseEmbedding

Cited by

7 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceT2Space