Theorems · Theorem · general topology
Topology.IsEmbedding.isLocallyClosed_iff
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} {f : X → Y},
Topology.IsEmbedding f → (IsLocallyClosed s ↔ ∃ s', IsLocallyClosed s' ∧ s' ∩ Set.range f = f '' s)- Defined in
- Mathlib.Topology.LocallyClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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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.imagestatement and proof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- Topology.IsEmbeddingstatement and proof · cited by 294
- Set.image_preimage_eq_inter_rangeproof · cited by 121
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsEmbedding.isInducingproof · cited by 47
- IsLocallyClosedstatement and proof · cited by 44
- Set.image_injectiveproof · cited by 15
- Topology.IsInducing.isLocallyClosed_iffproof · cited by 2
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