Theorems · Theorem · general topology
IsOpenQuotientMap.locallyCompactSpace
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [LocallyCompactSpace X]
{f : X → Y}, IsOpenQuotientMap f → LocallyCompactSpace Y- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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
- Set.imageproof · cited by 5,609
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- IsCompactproof · cited by 1,282
- LocallyCompactSpacestatement and proof · cited by 324
- Continuous.continuousAtproof · cited by 297
- Function.Surjective.forallproof · cited by 214
- Set.image_subset_iffproof · cited by 203
- IsCompact.imageproof · cited by 105
- IsOpenQuotientMapstatement and proof · cited by 65
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