Theorems · Theorem · general topology

Topology.IsClosedEmbedding.restrictPreimage

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} (s : Set β),
  Topology.IsClosedEmbedding f → Topology.IsClosedEmbedding (s.restrictPreimage f)

Alias of Set.restrictPreimage_isClosedEmbedding.

Defined in: Mathlib.Topology.LocalAtTarget
Cited by: 0 results in Mathlib
Foundations: Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace

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Setstatement · cited by 53,352
TopologicalSpacestatement · cited by 24,529
Set.Elemstatement · cited by 7,166
Set.preimagestatement · cited by 4,946
Topology.IsClosedEmbeddingstatement · cited by 195
Set.restrictPreimagestatement · cited by 84
Set.restrictPreimage_isClosedEmbeddingproof · cited by 1

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