Theorems · Theorem · general topology

Topology.IsEmbedding.restrict

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  Topology.IsEmbedding f →
    ∀ {s : Set X} {t : Set Y} (H : Set.MapsTo f s t), Topology.IsEmbedding (Set.MapsTo.restrict f s t H)

Defined in: Mathlib.Topology.Constructions
Cited by: 1 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Set.Elemstatement · cited by 7,166
Set.MapsTostatement and proof · cited by 732
Topology.IsEmbeddingstatement and proof · cited by 294
continuous_subtype_valproof · cited by 159
Set.MapsTo.restrictstatement · cited by 57
Topology.IsEmbedding.continuousproof · cited by 51
Topology.IsEmbedding.subtypeValproof · cited by 41
Topology.IsEmbedding.compproof · cited by 29
Topology.IsEmbedding.of_compproof · cited by 16
Continuous.restrictproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

Topology.IsOpenEmbedding.restrictproof · cited by 2