Theorems · Theorem · general topology

Topology.IsOpenEmbedding.baireSpace

∀ {X : Type u_1} [inst : TopologicalSpace X] [BaireSpace X] {Y : Type u_4} [inst_2 : TopologicalSpace Y] {p : Y → X},
  Topology.IsOpenEmbedding p → BaireSpace Y

If p : Y → X is an open embedding and X is a Baire space, then Y is a Baire space.

Defined in

Mathlib.Topology.Baire.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceBaireSpaceTopologicalSpace