Theorems · Theorem · general topology

ContinuousOn.isSeparable_image

∀ {β : Type v} {α : Type u_2} [inst : TopologicalSpace α] [TopologicalSpace.PseudoMetrizableSpace α]
  [inst_2 : TopologicalSpace β] {f : α → β} {s : Set α},
  ContinuousOn f s → TopologicalSpace.IsSeparable s → TopologicalSpace.IsSeparable (f '' s)

If a map is continuous on a separable set s, then the image of s is also separable.

Defined in

Mathlib.Topology.MetricSpace.Pseudo.Basic

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceTopologicalSpace