Theorems · Theorem · general topology

Topology.IsClosedEmbedding.IsCompletelyPseudoMetrizableSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [TopologicalSpace.IsCompletelyPseudoMetrizableSpace Y] {f : X → Y},
  Topology.IsClosedEmbedding f → TopologicalSpace.IsCompletelyPseudoMetrizableSpace X

Given a closed embedding into a completely pseudometrizable space, the source space is also completely pseudometrizable.

Defined in

Mathlib.Topology.Metrizable.CompletelyMetrizable

Cited by

1 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace.IsCompletelyPseudoMetrizableSpace