Theorems · Theorem · general topology
Topology.IsClosedEmbedding.weaklyLocallyCompactSpace
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [WeaklyLocallyCompactSpace Y]
{f : X → Y}, Topology.IsClosedEmbedding f → WeaklyLocallyCompactSpace X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- IsCompactproof · cited by 1,282
- Continuous.continuousAtproof · cited by 297
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- WeaklyLocallyCompactSpacestatement and proof · cited by 35
- WeaklyLocallyCompactSpace.exists_compact_mem_nhdsproof · cited by 28
- Topology.IsClosedEmbedding.continuousproof · cited by 25
- Topology.IsClosedEmbedding.isCompact_preimageproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- IsClosed.weaklyLocallyCompactSpaceproof · cited by 0