Theorems · Theorem · general topology

IsDenseInducing.inseparable_extend

∀ {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] [R1Space γ] (di : IsDenseInducing i) {f : α → γ} {a : α},
  ContinuousAt f a → Inseparable (di.extend f (i a)) (f a)

Defined in

Mathlib.Topology.DenseEmbedding

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceR1Space