Theorems · Theorem · general topology

isLocalHomeomorphOn_iff_isOpenEmbedding_restrict

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (s : Set X) {f : X → Y},
  IsLocalHomeomorphOn f s ↔ ∀ x ∈ s, ∃ U ∈ nhds x, Topology.IsOpenEmbedding (U.domRestrict f)

Defined in

Mathlib.Topology.IsLocalHomeomorph

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace