Theorems · Theorem · general topology

Dense.continuous_extend

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s : Set α} {f : ↑s → β}
  [T3Space β] (hs : Dense s),
  (∀ (a : α), ∃ b, Filter.Tendsto f (Filter.comap Subtype.val (nhds a)) (nhds b)) → Continuous (hs.extend f)

Defined in

Mathlib.Topology.DenseEmbedding

Cited by

0 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT3Space