Theorems · Theorem · general topology

IsDenseInducing.continuous_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] [T3Space γ] {f : α → γ} (di : IsDenseInducing i),
  (∀ (b : β), ∃ c, Filter.Tendsto f (Filter.comap i (nhds b)) (nhds c)) → Continuous (di.extend f)

Defined in

Mathlib.Topology.DenseEmbedding

Cited by

5 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceT3Space