Theorems · Theorem · general topology
Topology.IsOpenEmbedding.locallyCompactSpace
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [LocallyCompactSpace Y]
{f : X → Y}, Topology.IsOpenEmbedding f → LocallyCompactSpace X- Cited by
- 3 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LocallyCompactSpacestatement and proof · cited by 324
- Topology.IsOpenEmbeddingstatement and proof · cited by 231
- Topology.IsOpenEmbedding.isOpen_rangeproof · cited by 33
- IsOpen.isLocallyClosedproof · cited by 20
- Topology.IsOpenEmbedding.isInducingproof · cited by 14
- Topology.IsInducing.locallyCompactSpaceproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- LocallyCompactSpace.of_finiteDimensional_of_completeproof · cited by 1
- Homeomorph.locallyCompactSpace_iffproof · cited by 0
- TopologicalSpace.Compacts.locallyCompactSpace_iffproof · cited by 0