Theorems · Theorem · general topology

Topology.IsInducing.isLocallyClosed_iff

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} {f : X → Y},
  Topology.IsInducing f → (IsLocallyClosed s ↔ ∃ s', IsLocallyClosed s' ∧ f ⁻¹' s' = s)

Defined in

Mathlib.Topology.LocallyClosed

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace